Masafumi Fukuma

String field theory from IIB matrix model

Abstract We derive Schwinger-Dyson equations for the Wilson loops of IIB matrix model. Superstring coordinates are introduced through the construction of the loop space. We show that the continuum limit of the loop equation reproduces the light-cone superstring field theory of type IIB superstring in the large-N limit. We find that the interacting string theory can be obtained in the double scaling limit as it is expected.

Comments on T-Dualities of Ramond-Ramond Potentials

The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions including the Chern-Simons term.

A Note on the Weyl Anomaly in the Holographic Renormalization Group

We give a prescription for calculating the holographic Weyl anomaly in arbitrary dimension within the framework based on the Hamilton-Jacobi equation proposed by de Boer, Verlinde and Verlinde. A few sample calculations are made and shown to reproduce the results that are obtained to this time with a different method. We further discuss continuum limits, and argue that the holographic renormalization group may describe the renormalized trajectory in the parameter space. We also clarify the relationship of the present formalism to the analysis carried out by Henningson and Skenderis.

Combinatorics of solitons in noncritical string theory

We study the combinatorics of solitons in D < 2 (or c < 1) string theory. The weights in the summation over multi-solitons are shown to be automatically determined if we further require that the partition function with soliton background be a τ function of the KP hierarchy, in addition to the W1 + ∞ constraint.

Nonperturbative effects in noncritical strings with soliton backgrounds

We explicitly construct soliton operators in D < 2 (or c < 1) string theory, and show that the Schwinger-Dyson equations allow solutions with these solitons as backgrounds. The dominant contributions from 1-soliton background are explicily evaluated in the weak coupling limit, and shown to agree with the nonperturbative analysis of string equations. We suggest that fermions should be treated as fundamental dynamical variables since both macroscopic loops and solitons are constructed in their bilinear forms.

Higher-Derivative Gravity and the AdS/CFT Correspondence

We investigate the AdS/CFT correspondence for higher-derivative gravity systems, and develop a formalism in which the generating functional of the boundary field theory is given as a functional that depends only on the boundary values of bulk fields. We also derive a Hamilton-Jacobi-like equation that uniquely determines the generating functional, and give an algorithm calculating the Weyl anomaly. Using the expected duality between a higher-derivative gravity system and N=2 superconformal field theory in four dimensions, we demonstrate that the resulting Weyl anomaly is consistent with the field theoretic one.

COMMENTS ON D-INSTANTONS IN C< 1 STRINGS

We suggest that the boundary cosmological constant ζ in c<1 unitary string theory be regarded as the one-dimensional complex coordinate of the target space on which the boundaries of world-sheets can live. From this viewpoint we explicitly construct analogues of D-instantons which satisfy Polchinskis “combinatorics of boundaries.” We further show that our operator formalism developed in the preceding articles is powerful in evaluating D-instanton effects, and also demonstrate for simple cases that these effects exactly coincide with the stringy nonperturbative effects found in the exact solutions of string equations.

Representation Theory of The W1+∞ Algebra ∗

We review the recent development in the representation theory of the

Eigensystem and full character formula of theW1+∞ algebra withc = 1

W_{1+infty}

Character and determinant formulae of quasifinite representation of theW1+∞ algebra

algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as