World-Sheet String Duality and the Hidden Supersymmetry

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.Comment: 12 pages, talk presented at the 10th International Symposium on String Theory (July 3-7, Fukuoka, Japan, 2001) and a part of lectures given at the Summer Conference on Strings (July 16-27, Beijing, China, 2001

Holography in the Large J Limit of AdS/CFT Correspondence and Its Applications

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 Dp-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.Comment: 21 pages, written version of a talk given at the symposium "Frontiers of Quantum Science", YITP, Kyoto, Feb. 2005, corrected typos and some minor revisions of tex

Field Theory of Yang-Mills Quantum Mechanics for D Particles

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.Comment: corrected typos, corrected references, 39 pages, 2 figures, version to be published in Prog. Theor. Phy

Supergravity, AdS/CFT Correspondence and Matrix Models

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.Comment: Expanded and combined version of two talks given at Nishinomiya-Yukawa Symposium, Nov., 1998 and YITP workshop, Nov., 1998, 23 pages, no figures (revision: sentences and references are added to clarify the relation between the space-time uncertainty relation and holography

What is Holography in the Plane-Wave Limit of AdS/CFT Correspondence ?

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 Euclidean S-matrix in the bulk and the short-distance operator-product expansion of the so-called BMN operators on the boundary.Comment: 17 pages, 2 figures, an expanded written version of talk at the Nishinomiya Yukawa Memorial Symposium, Nishinomiya, November, 200

String Theory : Where are we now?

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.Comment: 19 pages, 1 figure, written version of a general talk in the workshop "Frontier of Theoretical Physics", Beijing, Nov, 1999, minor typos correcte