arXiv subjects

Hiroshi Shirokura

Publications and source records attributed to Hiroshi Shirokura.

5 recordsLinked to original sources

arXiv1996

Exact Solution of 1-matrix Model

I review my new method for solving general 1-matrix models by expanding in $N^{-1}$ without taking a physical continuum limit. Using my method, each coefficient of the free energy in the genus expansion is exactly computable. One can include physical information in a function which is uniquely specified by the action of the model. My method gives completely the same result with the usual one if the physical fine tuning is done and the leading singular terms are extracted. I also calculate in the genus three case and confirm the validity of my method.

hep-th↗

arXiv1995

Generating Functions in Two Dimensional Quantum Gravity

We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more higher genus. Each generating function can be expressed by a ``specific heat'' function for sphere. Universal terms, which are survived in the double scaling limit can be easily picked out from our exact solutions. We also find that the regular part of the spherical generating function is at most bilinear in coupling constants of source terms.

hep-th↗

arXiv1994

Modification of Matrix Models by Square Terms of Scaling Operators

We study one (or two) matrix models modified by terms of the form $g(ρ(P))^2 + g'(ρ'({\cal{O}}))^2$, where the matrix representation of the puncture operator $P$ and the one of a scaling operator ${\cal{O}}$ are denoted by $ρ(P)$ and $ρ'({\cal{O}})$ respectively. We rewrite the modified models as effective theories of baby universes. We find an upper bound for the gravitational dimension of ${\cal{O}}$ under which we can fine tune the coupling constants to obtain new critical behaviors in the continuum limit. The simultaneous tuning of $g$ and $g'$ is possible if the representations $ρ(P)$ and $ρ'({\cal{O}})$ are chosen so that the non-diagonal elements of the mass matrix of the effective theory vanish.

hep-th↗

arXiv1993

Factorization in 2D String Theory

We show the factorization of correlation functions of tachyon operators in 2D string theory using the discretized approach of Moore. Our demonstration of the factorization is more general than that of the paper of Sakai and Tanii. We obtain the rules for the factorization of tachyon amplitudes. Our results can be understood in terms of the operator product expansion of tachyon operators. We also give a systematic way of computing correlation functions of tachyon operators and succeed in summarizing the results of the computation in compact form for some simple cases. We confirm that these tachyon amplitudes indeed satisfy our factorization rule.

hep-th↗

arXiv1993

Macroscopic Loop Amplitudes in Two-Dimensional Dilaton Gravity

Macroscopic loop amplitudes are obtained for the dilation gravity in two-dimensions. The dependence on the macroscopic loop length $l$ is completely determined by using the Wheeler-DeWitt equation in the mini-superspace approximation. The dependence on the cosmological constant $Λ$ is also determined by using the scaling argument in addition.

hep-th↗