• Direct test of the gauge-gravity correspondence for Matrix theory correlation functions
  • M. Hanada (Physics Dept., University of Washington), J. Nishimura (KEK Theory Center), Y. Sekino (KEK Theory Center), and T. Yoneya (School of Graduate Studies, The Open University of Japan)
  • JHEP 1112(2011)020 (arXiv:1108.5153[hep-th] )
  Abstract We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) Yang-Mills theory, which was proposed by Banks et al. as a non-perturbative definition of 11-dimensional M-theory in the infinite-momentum frame. We perform firstprinciple calculations using Monte Carlo simulations, and compare the results against the predictions obtained previously based on the gauge-gravity correspondence from 10 dimensions. After providing a self-contained review on these predictions, we present clear evidence that the predictions in the large-N limit actually hold even at small N such as N = 2 and 3. The predicted behavior seems to continue to the far infrared regime, which goes beyond the naive range of validity of the 10D supergravity analysis. This suggests that the correlation functions also contain important information on the M-theory limit.

• Towards Quantum Field Theory of D-Particles
  • Tamiaki Yoneya (School of Graduate Stadies, The Open University of Japan)
  • Prog. Theor. Phys. Suppl. 188, 63-74 (2011). Invited talk at the ``International Conference on String Field Theory and Related Aspects" (SFT2010) Oct 18-22, Kyoto, Japan
  Abstract In my talk in the workshop, I have summarized my recent attempt towards a quantum field theory of D-particles (or D0-branes). Since the main paper and some reviewing papers on this subject have already been published, I think that there is no point in repeating the previous discussions in this report. Instead, I give my personal view on the status of string field theory from a historical perspective, as well as the motivation toward the new attempt aiming a field theory of D-particles.

• Monte Carlo studies of Matrix theory correlation functions
  • Masanori Hanada (Weizmann Institute of Science), J. Nishimura (KEK), Yaruhiro Sekino (Okayama Inst. Quantum Physics), and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Phys. Rev. Lett. 104(2010), 151601 (arXiv:0911.1623 [hep-th]
  Abstract We study correlation functions in (0+1)-dimensional maximally supersymmetric U(N) gauge theory, which represents the low-energy effective theory of D0-branes. In the large-N limit, the gauge-gravity duality predicts power-law behaviors in the infrared region for the two-point correlation functions of operators corresponding to supergravity modes. We evaluate such correlation functions on the gauge theory side by the Monte Carlo method. Clear power-law behaviors are observed at N=3, and the predicted exponents are confirmed consistently. Our results suggest that the agreement extends to the M-theory regime, where the supergravity analysis in 10 dimensions

• Gravity from strings: personal reminiscences of early developments
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • arXiv:0901.0079. Invited contribution to the book ``The Birth of String Theory", Cambridge University Press (April, 2012), ISDN:9780521197908.
  Abstract I discuss the early developments of string theory with respect to its connection with gauge theory and general relativity from my own perspective. The period covered is mainly from 1969 to 1974, during which I became involved in research on dual string models as a graduate student. My thinking towards the recognition of string theory as an extended quantum theory of gravity is described. Some retrospective remarks on my later works related to this subject are also given.

• An Attempt Towards Field Theory of D0 Branes -- Quantum M-Field Theory --
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Int.J.Mod.Phys.A23:2343-2351,2008: arXiv:0804.0297 [hep-th], April, 2008. Invited talk presented at the workshop ``International Conference on Progress of String Theory and Quantum Field Theory", Osaka City University, December, 2007.
  Abstract: I discuss my recent attempt in search of a new framework for quantum field theory of D branes. After explaining some motivations in the background of this project, I present, as a first step towards our goal, a second-quantized reformulation of the U($N$) Yang-Mills quantum mechanics in which the D0-brane creation-and-annihilation fields connecting theories with different $N$ are introduced. Physical observables are expressed in terms of bilinear forms of the D0 fields. The large $N$ limit is briefly treated using this new formalism.

• Space-Time Uncertainty and Approaches to D-Brane Field Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Prog.Theor.Phys.Suppl.171:87-98,2007: arXiv:0706.0642 [hep-th], June, 2007. Written version of an invited talk presented at the 21st Nishinomiya-Yukawa Symposium, Nishinomiya-Kyoto, YITP, Nov. 2006.
  Abstract: In connection with the space-time uncertainty principle which gives a simple qualitative characterization of non-local or non-commutative nature of short-distance space-time structure in string theory, author's recent approaches toward field theories for D-branes are briefly outlined, putting emphasis on some key ideas lying in the background. The final section of the present report is devoted partially to a tribute to Yukawa on the occasion of the centennial of his birth.

• String Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • J.Phys.Soc.Jap.76:111020,2007. Invited review article (written in Jan. 2007), published on a special issue of Journal of the Physical Society of Japan
  Abstract: This article is devoted to a nontechnical review on the present status of string theory towards an ultimate unification of all fundamental interactions including gravity. In particular, we emphasize the importance of string theory as a new theoretical framework in which the long-standing conflict between quantum theory and general relativity is resolved.

• Field Theory of Yang-Mills Quantum Mechanics for D-Particles
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Prog. Theor. Phys. 118, 135-167(2007), arXiv: 0705:1960 [hep-th]
  Abstract: We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D-particles in a Fock space of U(N) Yang-Mills theories with all different N in a unified way. D-particle field operators, creating and annihilating a D-particle and hence changing N one by one, are defined. The base space of these D-particle fields is a (complex) vector space of infinite dimensions. The gauge invariance of Yang-Mills quantum mechanics is reinterpreted as a quantum-statistical symmetry, which is taken into account by setting up a novel algebraic and projective structure in the formalism. Ordinary physical observables of Yang-Mills theory, obeying the standard algebra, are expressed as bilinear forms of the D-particle fields. Together with the open-closed string duality, our new formulation suggests a trinity of three different but mutually dual viewpoints in string theory.

• 1/2-BPS Correlators as c=1 S-matrix
  • Antal Jevicki (Brown Univ.) and Tamiaki Yoneya (U. Tokyo, Komaba)
  •  JHEP03:001,2007 (hep-th/0612262, December, 2006).
  Abstract: We argue from two complementary viewpoints of Holography that the 2-point correlation functions of 1/2-BPS multi-trace operators in the large-N (planar) limit are nothing but the (Wick-rotated) S-matrix elements of c=1 matrix model. On the bulk side, we consider an Euclideanized version of the so-called bubbling geometries and show that the corresponding droplets reach the conformal boundary. Then the scattering matrix of fluctuations of the droplets gives directly the two-point correlators through the GKPW prescription. On the Yang-Mills side, we show that the two-point correlators of holomorphic and anti-holomorphic operators are essentially equivalent with the transformation functions between asymptotic in- and out-states of c=1 matrix model. Extension to non-planar case is also discussed.

• Holography of Wilson-Loop Expectation Values with Local Operator Insertions
  • Akitsugu Miwa and Tamiaki Yoneya (U. Tokyo, Komaba)
  •  JHEP 0612:060,2006 (hep-th/0609007, September, 2006).
  Abstract: We study the expectation values of Wilson-loop operators with the insertions of local operators Z^J and barZ^J for large J from the bulk viewpoint of AdS/CFT correspondence. Classical solutions of strings attached to such deformed Wilson loops at the conformal boundary are constructed and are applied to the computation of Wilson-loop expectation values. We argue that in order to have such solutions for general insertions at finite positions in the base spacetime of the gauge theory, it is crucial to interpret the holographic correspondence in the semi-classical picture as a tunneling phenomenon, as has been previously established for holographic computations of correlators of BMN operators. This also requires to use the Euclideanized AdS background and Euclidean super Yang-Mills theory.

• Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Prog. Theor. Phys. Suppl. 164(2006) 82-102, hep-th/0607046. This article is based on an invited talk given by the present author in the symposium, ``Frontiers of Quantum Science", YITP, Kyoto University, February, 2005.
  Abstract: We give a brief expository discussion on the holographic correspondence of correlation functions in the large-$J$ limit of AdS/CFT conjecture. We first review our proposals on the interpretation of the so-called GKPW relation in the large-$J$ limit or BMN limit, which are based upon a tunneling picture in relating the AdS bulk to its boundary. Some concrete results, explicitly confirming our picture, are summarized. We then proceed to comment on various issues related to this subject, such as extension of the present picture to nonconformal D$p$-brane backgrounds, the correlators of deformed Wilson loops, spinning-string/spin-chain correspondence, and the inclusion of higher string-loop effects. In particular, as for the deformation of Wilson loops, we present a typical tunneling world-sheet solution which can be used for direct derivation of the expectation values of deformed Wilson loops following our picture.

• Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • JHEP 12(2005)028, hep-th/0510114.
  Abstract: We extend the fermion representation of single-charge 1/2-BPS operators in the four-dimensional N=4 super Yang-Mills theory to general (multi-charge) 1/2-BPS operators such that all six directions of scalar fields play roles on an equal footing. This enables us to construct a field-theorectic representation for a second-quantized system of spherical D3-branes in the 1/2-BPS sector. The Fock space of D3-branes is characterized by a novel exclusion principle (called `Dexclusion' principle), and also by a nonlocality which is consistent with the spacetime uncertainty relation. The Dexclusion principle is realized by composites of two operators, obeying the usual canonical anticommutation relation and the Cuntz algebra, respectively. The nonlocality appears as a consequence of a superselction rule associated with a symmetry which is related to the scale invariance of the super Yang-Mills theory. The entropy of the so-called superstars, with multiple charges, which have been proposed to be geometries corresponding to the condensation of giant gravitons is discussed from our viewpoint and is argued to be consistent with the Dexclusion principle. Our construction may be regarded as a first step towards a possible new framework of general D-brane field theory.

• Impurity Non-Preserving 3-Point Correlators of BMN Operators from PP-Wave Holography I : Bosonic Excitations
  • Suguru Dobashi and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B711:54-82 (2005), hep-th/0409058.
  Abstract: As a continuation of our previous works studying the holographic principle in the plane-wave limit, we discuss the 3-point correlation functions of BMN operators with bosonic excitations when impurities are not conserved. We show that our proposal for a holographic mapping between the conformal OPE coefficients of super Yang-Mills theory and the 3-point vertex of the holographic string field theory is valid to the leading order in the large $\mu$ limit. Our results provide for the first time a direct holographic relation for the 3-point correlators of BMN operators including impurity non-preserving processes.

• Resolving the Holography in the Plane-Wave Limit of AdS/CFT Correspondence
  • Suguru Dobashi and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B711:3-53 (2005), hep-th/0406225.
  Abstract: The issue of holographic mapping between bulk and boundary in the plane-wave limit of AdS/SYM correspondence is reexamined from the viewpoint of correlation functions. We first study the limit of large angular momentum for the so-called GKP-W relation in supergeravity approximation, connecting directly the effective action in the bulk and the generating functional of correlation functions on the boundary. The spacetime tunneling picture which has been proposed in our previous works naturally emerges. This gives not only a justification of our previous proposal, with some important refinements, on the mapping between bulk effective interaction and the CFT coefficients on the boundary in the plane-wave limit, but also implies various insights on the interpretation of holography in the plane-wave limit. Based on this result, we construct a new `holographic' string field theory. We confirm for several nontrivial examples that this gives the CFT coefficients derived by perturbation theory on the gauge-theory side. Our results are useful for understanding how apparently different duality maps proposed from different standpoints are consistent with each other and with our definite spacetime picture for the AdS holography in the plane-wave limit.

• PP-Wave Holography for Dp-Brane Backgrounds
  • Masako Asano(KEK), Yasuhiro Sekino (KEK), and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B678:197-232 (2004). hep-th/0308024.
  Abstract: As an extension of the so-called BMN conjecture, we investigate the plane-wave limit for possible holographic connection between bulk string theories in non-conformal backgrounds of D$p$-branes and the corresponding supersymmetric gauge theories for $p<5$. Our work is based on the tunneling picture for dominant null trajectories of strings in the limit of large angular momentum. The tunneling null trajectories start from the near-horizon boundary and return to the boundary, and the resulting backgrounds are time-dependent for general D$p$-branes except for $p=3$. We develop a general method for extracting diagonalized two-point functions for boundary theories as Euclidean (bulk) S-matrix in the time-dependent backgrounds. For the case of D0-brane, two-point functions of supergravity modes are shown to agree with the results derived previously by the perturbative analysis of supergravity. We then discuss the implications of the holography for general cases of D$p$-branes including the stringy excitations. All the cases ($p\ne 3, p<5$) exhibit interesting infra-red behaviors, which are different from free-field theories, suggesting the existence of quite nontrivial fixed-points in dual gauge theories.

• What is Holography in the Plane-Wave Limit of the AdS/SYM Correspondence ?
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/0304183. This expository article is based on the invited talk ``Holography and the Plane-Wave Limit of the AdS/CFT Correspondence" given by the present author at the Yukawa Memorial Symposium, November, Nishinomiya, 2002. The present version is considerably expanded and corrected from the one to be published in the Proceedings (Prog. Theor. Phys. Suppl. 152: 108-120 (2003).
  Abstract: The issue of holographic principle in the PP-wave limit of the AdS/CFT correspondence is discussed, in the hope of clarifying some confusions in the literature. We show that, in the plane-wave limit, the relation between the partition function in the bulk and the gauge-invariant correlation functions on the boundary should be interpreted on the basis of a tunneling picture in the semi-classical approximation which is appropriate for the plane-wave limit. This leads to a natural relation between {\it Euclidean} S-matrix in the bulk and the short-distance operator-product expansion of the so-called BMN operators on the boundary.

• From Wrapped Supermembrane to M(atrix) Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Invited talk presented at the 3rd Sakharov International Conference on Physics, Moscow, June, 2002; hep-th/0210243. Published in the Proceedings : 631-644 (2003).
  Abstract: The issue of justifying the matrix-theory proposal is revisited. We first discuss how the matrix-string theory is derived directly starting from the eleven dimensional supermembrane wrapped around a circle of radius $R=g_s\ell_s$, without invoking any stringy assumptions, such as S- and T-dualities. This derivation provides us a basis for studying both string ($R\rightarrow 0)$- and M ($R\rightarrow \infty$)-theory limits of quantum membrane theory in a single unified framework. In particular, we show that two different boosts of supermembrane, namely one of unwrapped membrane along the M-theory circle and the other of membrane wrapped about a transervse direction which is orthogonal to the M-theory circle, give the same matrix theory in the 11 dimensional limit, $R\rightarrow \infty$ (with $N\rightarrow \infty$). We also discuss briefly the nature of possible covariantized matrix (string) theories.

• Holographic Reformulation of String Theory on AdS$_5\times$S$^5$ background in the PP-wave limit
  • Suguru Dobashi, Hidehiko Shimada, and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B665:94-128, 2003(hep-th/0209251).
  Abstract: The recent proposal on the correspondence between the ${\cal N}=4$ super Yang-Mills theory and string theory in the Penrose limit of the AdS$_5\times$S$^5$ geometry involves a few puzzles from the viewpoint of holographic principle, especially in connection with the interpretation of times. To resolve these puzzles, we propose to interpret the PP-wave strings on the basis of tunneling null geodesics connecting boundaries of the AdS geometry. Our approach predicts a direct and systematic identification of the S-matrix of Euclidean string theory in the bulk with the short-distance structure of correlation functions of super Yang-Mills theory on the AdS boundary, as an extension of the ordinary relation in supergravity-CFT correspondence. Holography requires an infinite number of contact terms for interaction vertices of string field theory and constrains their forms in a way consistent with supersymmetry.

• String Theory and Gravitation
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Invited lecture presented at the workshop "Noncommutative Differential Geometry and its Application to Physics" (May 31- June 4, Shonan, 1999), Prog. Theor. Phys. Suppl. 144: 176--194 (2001).
  Abstract: This is an abbreviated written version of pedagogical lectures delivered in the workshop "Noncommutative Differential Geometry and its Application to Physics" (Shonan, May 31-June 4, 1999). The purpose was to give an overview on the nature of string theory as quantum gravity. After giving a brief historical introduction, we discuss how general relativity can be derived as consistent local field theory of massless spin 2 particle in the low-energy limit. Then, several important issues, such as the manner how string theory contains gravity, the stringy resolution of ultraviolet difficulty, duality between open and closed strings, are critically reviewed.

• String Theory and the Uncertainty Principle
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Invited paper in Current Science Vol. 81 (2001)1554-1560 (Indian Academy of Science)
  Abstract: String theory has been pursued as the prime possibility towards the fundamental theory of matter, spacetime and all natural forces including gravity. It suggests a way by which the traditional notion of continuum spacetime is modified at short distance regime such that relativity and quantum theory might finally be unified. We discuss the possible significance of this aspect of string theory from a historical perspective, focusing on the uncertainty principle.

• World-Sheet String Duality and the Hidden Supersymmetry
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/0109058, September 2001, Invited talk presented at the 10th International Symposium on String Theory (July 3-7, Fukuoka, Japan, 2001), published in the Proceedings (Americal Institute of Physics Proceedings 607:279-289(2002), eds. H. Aoki and T. Tada), and a part of lectures given at the Summer Conference on Strings (July 16-27, Beijing, China, 2001).
  Abstract: It is reviewed how space-time supersymmetry is realized nonlinearly in open superstring theory without making the GSO projection. We show that the world-sheet string dualities, viz. dualities of open-closed strings and of open-open strings, play crucial roles for the existence of 10 dimensional N=2 supersymmetry in a spontaneously broken phase. We also speculate on a possible mechanism of the restoration of supersymmetry from the viewpoint of world-sheet dynamics.

• From Supermembrane to Matrix String
  • Yasuhiro Sekino (TIT) and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B619:22-50, 2001 (hep-th/0108176, August, 2001).
  Abstract: We develop a systematic method of directly embedding supermembrane wrapped around a circle into matrix string theory. Our purpose is to study connection between matrix string and membrane from an entirely 11 dimensional point of view. The method does neither rely upon the DLCQ limit nor upon string dualities. In principle, this enables us to construct matrix string theory with arbitrary backgrounds from the corresponding supermembrane theory. As a simplest application of the formalism, the matrix-string action with a 7 brane background (Kaluza-Klein Melvin solution) with nontrivial RR vector field is given.

• Nonlinear Supersymmetry without the GSO Projection and Unstable D9-Brane
  • Tabito Hara and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B602:499-513, 2001 (hep-th/0010173, October, 2000)
  Abstract: Orientable open string theories containing both bosons and fermions without the GSO projection are expected to have the 10 dimensional $N=2$(A) space-time supersymmetry in a spontaneously broken phase. We study the low-energy theorem for the nonlinearly realized $N=2$ supersymmetry using the effective action for an unstable D9-brane. It is explicitly confirmed that the 4-fermion open string amplitudes without the GSO projection obey the low-energy theorem derived from the nonlinear $N=2$ supersymmetry. An intimate connection between the existence of the hidden supersymmetry and the open-open string (s-t) duality is pointed out.

• Space-Time Uncertainty and Noncommutativity in String Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Int. J. Mod. Phys. A16: 945-956, 2001 (Invited talk at the Strings 2000 Conference, July, Univ. of Michigan, 2000, hep-th/0010172, October, 2000).
  Abstract: We analyze the nature of space-time nonlocality in string theory. After giving a brief overview on the conjecture of the space-time uncertainty principle, a (semi-classical) reformulation of string quantum mechanics, in which the dynamics is represented by the noncommutativity between temporal and spatial coordinates, is outlined. The formalism is then compared to the space-time noncommutative field theories associated with nonzero electric B-fields.

• String Theory and the Space-Time Uncertainty Principle
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Prog. Theor. Phys. 103: 1081--1125 (2000)(Invited paper)(hep-th/0004074, April, 2000).
  Abstract: The notion of space-time uncertainty principle in string theory is clarified and further developed. The motivation and the derivation of the principle are first reviewed in a reasonably self-contained way. It is then shown that the nonperturbative (Borel summed) high-energy and high-momentum transfer behaviors of string scattering are consistent with the space-time uncertainty principle. It is also shown that, in consequence of the principle, string theories in 10 dimensions generically exhibit a characteristic length scale which is equal to the well-known 11 dimensional Planck length $g_s^{1/3}\ell_s$ of M-theory as the scale at which stringy effects take over the effects of classical supergravity, even without involving D-branes directly. The meanings of the space-time uncertainty relation in connection with D-branes and black holes are discussed and reinterpreted. Finally, we present a novel interpretation of the Schild-gauge action for strings from a viewpoint of noncommutative geometry, which conforms to the space-time uncertainty relation by manifestly exhibiting a noncommutativity of quantized string coordinates dominantly between space and time. We also discuss the consistency of the space-time uncertainty relation with S and T dualities.

• STRING THEORY -- Where are we now? --
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/0004075, Feb., 2000, written version of invited plenary talk at the workshop "Frontier of Theoretical Physics", Beijing, November, 1999, published in the Proceedings (World Scientific), 59-74.
  Abstract: This is a brief overview on the current status of string theory for non-specialists. The purpose is to give an aspect on the nature of string theory as a unified theory of all interactions including quantum gravity and to discuss future perspectives. Particular emphases are put on the mysteries why string theory contains gravity and why it resolves the ultraviolet problems.

• Spontaneously Broken Space-Time Supersymmetry in Open String Theory without GSO Projection
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B. 576:219-240, 2000. (hep-th/9912255, December, 1999)
  Abstract: We argue that orientable open string theory without GSO projection has N=2 space-time supersymmetry in a spontaneously broken phase. The arguments are presented both in Neveu-Schwarz-Ramond and Green-Schwarz formulations. The formal but explicit supersymmetry transformation law for string field is given in the framework of Witten's open string field theory. Our results support a fundamental assumption which lies behind the topological construction of stable D-branes starting from the unstable systems of D9-branes.

• Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Classical and Quantum Gravity 17:1307-1316,2000. Written version of an invited talk presented at Strings'99 conference (Potsdam, July, 1999), hep-th/9908153 (August, 1999),
  Abstract: The large N behavior of Matrix theory is discussed on the basis of the previously proposed generalized conformal symmetry. The concept of `oblique' AdS/CFT correspondence, in which the conformal symmetry involves both the space-time coordinates and the string coupling constant, is proposed. Based on the explicit predictions for two-point correlators, possible implications for the Matrix-theory conjecture are discussed.

• Generalized AdS-CFT Correspondence for Matrix Theory in the Large N limit
  • Yasuhiro Sekino and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Nucl. Phys. B570:174-206. hep-th/9907029 (July, 1999).
  Abstract: Guided by the generalized conformal symmetry, we investigate the extension of AdS-CFT correspondence to the matrix model of D-particles in the large N limit. We perform a complete harmonic analysis of the bosonic linearized fluctuations around a heavy D-particle background in IIA supergravity in 10 dimensions and find that the spectrum precisely agrees with that of the physical operators of Matrix theory. The explicit forms of two-point functions give predictions for the large N behavior of Matrix theory with some special cutoff. We discuss the possible implications of our results for the large N dynamics of D-particles and for the Matrix-theory conjecture. We find an anomalous scaling behavior with respect to the large N limit associated to the infinite momentum limit in 11 dimensions, suggesting the existence of a screening mechanism for the transverse extension of the system.

• On the Quantization of Nambu Brackets
  • H. Awata (YITP, Kyoto), M. Li (EFI, Chicago), D. Minic(U. South. Cal.), and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9906248 (June, 1999), published in JHEP02:013-028, 2001.
  Abstract: We present several non-trivial examples of the three-dimensional quantum Nambu bracket which involve square matrices or three-index objects. Our examples satisfy two fundamental properties of the classical Nambu bracket: they are skew-symmetric and they obey the Fundamental Identity. We contrast our approach to the existing literature on the quantum deformations of Nambu mechanics. We also discuss possible applications of our results in M-theory.

• Supergravity, AdS/CFT Correspondence, and Matrix Models
  • Tamiaki Yoneya (U. Tokyo) , Prog. Theor. Phys. Suppl. 134(1999) 182-206. (Expanded version of invited talks given in Nishinomiya-Yukawa symposium and YITP worshop, November, 1998), hep-th/992200 (February, 1999).
  Abstract: The recent developments towards the possible non-perturbative formulation of string/M theory using supersymmetric Yang-Mills matrix models (SYMs) are discussed. In the first part, we give a critical review on the status of our present understanding, focusing on the connection of the D0-brane matrix models to supergravity and its relevance to the so-called Matrix-theory conjecture. We also discuss some problems concerning the conjectured relation between supergravity in AdS background and SYM from the viewpoint of D-brane interactions. We present a qualitative argument showing how the boundary condition at AdS boundary dictates the correlators on the large $N$ system of source D-branes. Then, in the final part, we turn to the question how to formulate the condensation of graviton in matrix models, taking the simplest example of type IIB matrix model. We argue the emergence of a hidden symmetry GL(10, R), beyond the manifest Lorentz symmetry SO(9,1), by embedding U($N$) model into models with higher $N$ and by treating the whole recursive series of models simultaneously. This suggests a possible approach toward background independent formulations of matrix models.

• Generalized Conformal Symmetry in D-Brane Matrix Models
  • Antal Jevicki (Brown Univ.), Yoichi Kazama and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9810146 (October, 1998), Phys. Rev. D59: 066001-1-12(1999).
  Abstract: We study in detail the extension of the generalized conformal symmetry proposed previously for D-particles to the case of supersymmetric Yang-Mills matrix models of Dp-branes for arbitrary p. It is demonstrated that such a symmetry indeed exists both in the Yang-Mills theory and in the corresponding supergravity backgrounds produced by Dp-branes. On the Yang-Mills side, we derive the field-dependent special conformal transformations for the collective coordinates of Dp-branes in the one-loop approximation, and show that they coincide with the transformations on the supergravity side. These transformations are powerful in restricting the forms of the effective actions of probe D-branes in the fixed backgrounds of source D-branes. Furthermore, our formalism enables us to extend the concept of (generalized) conformal symmetry to arbitrary configurations of D-branes, which can still be used to restrict the dynamics of D-branes. For such general configurations, however, it cannot be endowed a simple classical space-time interpretation at least in the static gauge adopted in the present formulation of D-branes.

• Equations of Motion and Galilei Invariance in D-Particle Dynamics
  • Yuji Okawa and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9808188 (August, 1998), Nucl. Phys. B541: 163-178(1999).
  Abstract: As a continuation of our previous work on the multi-body forces of D-particles in supergravity and Matrix theory, we investigate the problem of motion. We show that the scattering of D-particles including recoil derived in Matrix theory is precisely reproduced by supergravity with the discrete light-cone prescription up to the second order in 11 dimensional Newton constant. An intimate connection of recoil and Galilei invariance in supergravity is pointed out and elucidated.

• Quantum Metamorphosis of Conformal Transformation in D3-Brane Yang-Mills Theory
  • Antal Jevicki (Brown Univ.), Yoichi Kazama and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9808039 (August, 1998), Physical Review Letters 81:5072-5075, 1998.
  Abstract: We show how the linear special conformal transformation in four-dimensional $N=4$ super Yang-Mills theory is metamorphosed into the nonlinear and field-dependent transformation for the collective coordinates of Dirichlet 3-branes, which agrees with the transformation law for the space-time coordinates in the anti-de Sitter (AdS) space-time. Our result provides a new and strong support for the conjectured relation between AdS$_5 \times S^5$ supergravity and super conformal Yang-Mills theory (SYM). Furthermore, our work sheds elucidating light on the nature of the AdS/SYM correspondence.

• Short-Distance Space-Time Structure and Black Holes in String Theory : A Short Review of the Present Status
  • Miao Li (Einrico Fermi Inst. Univ. of Chicago) and Tamiaki Yoneya (U. Tokyo, Komaba) ,
  • Chaos, Solitons and Fractals 10(1999) 423--443 (Invited paper). hep-th/9806240 (June, 1998)
  Abstract: We briefly review the present status of string theory from the viewpoint of its implications on the short-distance space-time structure and black hole physics. Special emphases are given on two closely related issues in recent developments towards nonperturbative string theory, namely, the role of the space-time uncertainty relation as a qualitative but universal characterization of the short-distance structure of string theory and the microscopic formulation of black-hole entropies. We will also suggest that the space-time uncertainty relation can be an underlying principle for the holographic property of M theory, by showing that the space-time uncertainty relation naturally explains the UV/IR relation used in a recent derivation of the holographic bound for D3 brane by Susskind and Witten.

• Multi-Body Interactions of D-Particles in Supergravity and Matrix Theory
  • Yuji Okawa and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9806108 (June, 1998), Nuclear Physics B538:67-99, 1998.
  Abstract: We present detailed analyses of the 3-body interactions of D-particles from both sides of 11 dimensional supergravity and Matrix theory. In supergravity, we derive a complete expression for the classical bosonic effective action for D-particles including 2-and 3-body interaction terms. In Matrix theory, we compute 1-particle irreducible contributions to the eikonal phase shift in the two-loop approximation. The results precisely agree with the predictions from supergravity and thus provide a strong support to the discrete light-cone interpretation of the Matrix-theory conjecture as a possible nonperturbative definition of M-theory.

• Space-Time Uncertainty Principle and Conformal Symmetry in D-Particle Dynamics
  • Antal Jevicki (Brown Univ.) and Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9805069 (May, 1998), Nucl. Phys. B535: 335-348, 1998.
  Abstract: Motivated by the space-time uncertainty principle, we establish a conformal symmetry in the dynamics of D-particles. The conformal symmetry, combined with the supersymmetric non-renormalization theorem, uniquely determines the classical form of the effective action for a probe D-particle in the background of a heavy D-particle source, previously constructed by Becker-Becker-Polchinski-Tseytlin. Our results strengthen the conjecture proposed by Maldacena on the correspondence, in the case of D-particles, between the supergravity and the supersymmetric Yang-Mills matrix models in the large N-limit, the latter being the boundary conformal field theory of the former in the classical D-particle background in the near horizon limit.

• D-Particles, D-Instantons, and A Space-Time Uncertainty Principle in String Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • hep-th/9707002 (July, 1997), Invited talk given at the APCTP-ICTP Joint International Conference '97 (May 26-30, Seoul, Korea), published in Recent development in nonperturbative quantum field theory (World Scientific), pp286-303.
  Abstract: The purpose of this talk is to review some considerations by the present author on the possible role of a simple space-time uncertainty relation toward nonperturbative string theory. We first motivate the space-time uncertainty relation as a simple space-time characterization of the fundamental string theory. We then argue that the relation captures some of the important aspects of the short-distance dynamics of D-particles described by the effective super Yang-Mills matrix quantum mechanics, and also that the recently proposed type IIB matrix model can be regarded as a possible realization of the space-time uncertainty principle.

• Schild Action and Space-Time Uncertainty Principle in String Theory
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Prog. Theor. Phys. 97:949-961, 1997.
  Abstract: We show that the path-integral quantization of relativistic strings with the Schild action is essentially equivalent to the usual Polyakov quantization at critical space-time dimensions. We then present an interpretation of the Schild action which points towards a derivation of superstring theory as a theory of quantized space-time where the squared string scale, $\ell_s^2 \sim \alpha'$, plays the role of the minimum quantum for space-time areas. A tentative approach towards such a goal is proposed, based on a microcanonical formulation of large $N$ supersymmetric matrix model.

• Manifestly T-Duality Symmetric Matrix Models
  • Tsunehide Kuroki (U. Tokyo, Komaba), Yuji Okawa (U. Tokyo, Komaba), Fumihiko Sugino (KEK) and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Phys. Rev. D55:6429-6437, 1997.
  Abstract: We present a new class of matrix models which are manifestly symmetric under the T-duality transformation of the target space. The models may serve as a nonperturbative regularization for the T-duality symmetry in continuum string theory. In particular, it now becomes possible to extract winding modes explicitly in terms of extended matrix variables.

• D-Particle Dynamics and the Space-Time Uncertainty Relation
  • Miao Li (Enrico Fermi Institute) and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Published in Phys. Rev. Lett. 78: 1219-1222, 1997, with the title, "Pointlike D-brane Dynamics and Space-Time Uncertainty Relation".
  Abstract: We argue that the space-time uncertainty relation of the form $\Delta X \Delta T \gtrsim \alpha' $ for the observability of the distances with respect to time, $\Delta T$, and space, $\Delta X$, is universally valid in string theory including D-branes. This relation has been previously proposed by one (T.Y.) of the present authors as a simple qualitative representation of the perturbative short distance structure of fundamental string theory. We show that the relation, combined with the usual quantum mechanical uncertainty principle, explains the key qualitative features of D-particle dynamics.

• T-Duality Transformation and Universal Structure of Non-Critical String Field Theory
  • Takashi Asatani, Tsunehide Kuroki, Yuji Okawa, Fumihiko Sugino, and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Phys. Rev. D55: 5083-5111, 1997.
  Abstract: We discuss a T-duality transformation for the $c=1/2$ matrix model for the purpose of studying duality transformations in a possible toy example of nonperturbative frameworks of string theory. Our approach is to first investigate the scaling limit of the Schwinger-Dyson equations and the stochastic Hamiltonian in terms of the dual variables and then compare the results with those using the original spin variables. It is shown that the $c=1/2$ model in the scaling limit is T-duality symmetric in the sphere approximation. The duality symmetry is however violated when the higher-genus effects are taken into account, owing to the existence of global $\mbox{\boldmath $Z$}_2$ vector fields corresponding to nontrivial homology cycles. Some universal properties of the stochastic Hamiltonians which play an important role in discussing the scaling limit and have been discussed in a previous work by the last two authors are refined in both the original and dual formulations. We also report a number of new explicit results for various amplitudes containing macroscopic loop operators.

• STRING THEORY AND MATRIX MODELS.
  • Tamiaki Yoneya (U. Tokyo, Komaba)
  • Invited talk at the Internatinal Conference "Frontiers in Quantum Field Theory" (Commemoration of 60th birthday of Prof. Keiji Kikkawa), 14-17 Dec.(1995). hep-th/9603096 (December, 1995), Published in Frontiers in Quantum Field Theory (World Scientific, 1996), p178-189.
  Abstract: It is generally accepted that the double- scaled 1D matrix model is equivalent with the $c=1$ string theory with tachyon condensation. There remain however puzzles that are to be clarified in order to utilize this connection for our quest towards possible non-perturbative formulation of string theory. We discuss some of the issues that are related to the space-time interpretation of matrix model, in particular, the questions of leg poles, causality, and black hole background. I will finally speculate about a possible connection of a deformed matrix model with the idea of Dirichret branes

• STOCHASTIC HAMILTONIANS FOR NONCRITICAL STRING FIELD THEORIES FROM DOUBLE SCALED MATRIX MODELS.
  • Fumihiko Sugino and Tamiaki Yoneya (U. Tokyo, Komaba)
  • Phys.Rev.D53:4448-4488,1996.
  Abstract: We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest $c=0$ case, we derive the explicit forms of the Hamiltonians for the higher critical case $k=3$ (which corresponds to $c=-22/5$) and for the case $c=1/2$, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and $W_3$ algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.

• DOUBLING OF SCATTERING PHASE SHIFTS FOR TWO-DIMENSIONAL STRINGS.
  • Antal Jevicki, Miao Li (Brown U.) and Tamiaki Yoneya (U. Tokyo, Komaba).
  • Nucl.Phys.B448:277-292,1995.
  Abstract: We discuss the origin of the leg factors appearing in 2D string theory. Computing in the world sheet framework we use the semiclassical method to study string amplitudes at high energy. We show that in the case of a simplest 2-point amplitude these factors correspond entirely to the time delay for reflection off the Liouville wall. Our semiclassical calculation reveals that the string longitudinal modes, although nonpropagating in 2D spacetime, have the effect of doubling the phase shift. Particular emphasis is put on comparison with the point particle (center of mass) case. A general method is then given for calculating an arbitrary amplitude semiclassically.

• A DEFORMED MATRIX MODEL AND THE BLACK HOLE BACKGROUND IN TWO-DIMENSIONAL STRING THEORY.
  • Antal Jevicki (Santa Barbara, ITP & Brown U.) and Tamiaki Yoneya (Santa Barbara, ITP & U. Tokyo, Komaba).
  • Nucl.Phys.B411:64-96,1994.
  Abstract: We invesigate how the exact 2D black-hole solution for the critical string theory should be described, at least perturbatively with respect to the inverse mass of the black hole, within the framework of matrix model. In particular, we propose a working hypothesis on the basis of which we can present plausible candidates for the necessary non-local field redefinition of the tachyon field and the deformation of the usual $c=1$ matrix model with $\mu =0$. We exhibit some marked difference in the properties of tachyon scattering of the deformed model from those of the usual $c=1$ model corresponding to tachyon condensation. These results lead to a concrete proposal for the S-matrix for the tachyon black-hole scattering.

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