arXiv subjects
Publications and source records attributed to M. Fukuma.
We consider possible ambiguities in the holographic Weyl anomaly that are caused by local terms in the flow equation. We point out that such ambiguities actually do not give physically meaningful contributions to the Weyl anomaly.
We derive Schwinger-Dyson equations for the Wilson loops of a type 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.
We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.
We review the recent development in the representation theory of the $W_{1+\infty}$ algebra. The topics that we concern are, Quasifinite representation, Free field realizations, (Super) Matrix Generalization, Structure of subalgebras such as $W_\infty$ algebra, Determinant formula, Character formula. (Invited talk at ``Quantum Field Theory, Integrable Models and Beyond", YITP, 14-17 February 1994. To appear in Progress of Theoretical Physics Proceedings Supplement.)
We propose a new type of gauge in two-dimensional quantum gravity. We investigate pure gravity in this gauge, and find that the system reduces to quantum mechanics of loop length $l$. Furthermore, we rederive the $c\!=\!0$ string field theory which was discovered recently. In particular, the pregeometric form of the Hamiltonian is naturally reproduced.
We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the $\hat{\mbox{gl}}(\infty)$ algebra. As an example, we investigate the $\Win$ algebra which corresponds to the case $p(w)=w$, presenting its free field realizations and Kac determinants at lower levels.
We study quasifinite highest weight modules over the supersymmetric extension of the $W_{1+\infty}$ algebra on the basis of the analysis by Kac and Radul. We find that the quasifiniteness of the modules is again characterized by polynomials, and obtain the differential equations for highest weights. The spectral flow, free field realization over the $(B,C)$--system, and the embedding into $\Glinf$ are also presented.
We calculate the Kac determinant for the quasi-finite representation of \Winf algebra up to level 8. It vanishes only when the central charge is integer. We give an algebraic construction of null states and propose the character formulae. The character of the Verma module is related to free fields in three dimensions which has rather exotic modular properties.
By using the free field realizations, we analyze the representation theory of the W_{1+infinity} algebra with c=1. The eigenvectors for the Cartan subalgebra of W_{1+infinity} are parametrized by the Young diagrams, and explicitly written down by W_{1+infinity} generators. Moreover, their eigenvalues and full character formula are also obtained.
The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebras $R$, and the physical Hilbert space is identified with the center $Z(R)$ of the associative algebra $R$. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twisted $N=2$ minimal topological matter and the case where $R$ is a group ring.