Two-dimensional gravity, matrix models and nonperturbative string theory

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

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TWO-DIMENSIONAL QUANTUM GRAVITY, MATRIX MODELS AND STRING THEORY

International Journal of Modern Physics A ◽

10.1142/s0217751x93000497 ◽

1993 ◽

Vol 08 (07) ◽

pp. 1185-1244 ◽

Cited By ~ 4

Author(s):

KREŠIMIR DEMETERFI

Keyword(s):

String Theory ◽

Quantum Gravity ◽

Matrix Models ◽

Lattice Models ◽

Field Method ◽

Two Dimensional ◽

Large N ◽

The One ◽

Low Dimensional ◽

Lattice Approach

We review some results of the recent progress in understanding two-dimensional quantum gravity and low-dimensional string theories based on the lattice approach. The possibility to solve the lattice models exactly comes from their equivalence to large N matrix models. We describe various matrix models and their continuum limits, and discuss in some detail the phase structure of Hermitian one-matrix models. For the one-dimensional matrix model we discuss its field theoretic formulation through a collective field method and summarize some perturbative results. We compare the results obtained from matrix models to the results in the continuum approach to string theory.

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Matrix models of two-dimensional gravity and Toda theory

Nuclear Physics B ◽

10.1016/0550-3213(91)90482-d ◽

1991 ◽

Vol 357 (2-3) ◽

pp. 565-618 ◽

Cited By ~ 167

Author(s):

A. Gerasimov ◽

A. Marshakov ◽

A. Mironov ◽

A. Morozov ◽

A. Orlov

Keyword(s):

Matrix Models ◽

Two Dimensional ◽

Dimensional Gravity

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ON STRING THEORY INTERACTING WITH TWO-DIMENSIONAL GRAVITY

Modern Physics Letters A ◽

10.1142/s0217732394001155 ◽

1994 ◽

Vol 09 (15) ◽

pp. 1335-1343 ◽

Cited By ~ 1

Author(s):

I.L. BUCHBINDER ◽

I.L. SHAPIRO ◽

A.G. SIBIRYAKOV

Keyword(s):

String Theory ◽

Two Dimensional ◽

Dimensional Gravity ◽

The One

The approach is proposed to unification of the string theory and the two-dimensional gravity. Three classically equivalent forms are given. The one-loop counterterms are calculated in harmonic and conformal gauges. The relation between the counterterms for different classically equivalent variants of the theory and for the different gauge choices are studied.

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MATRIX MODELS AND NON-PERTURBATIVE STRING PROPAGATION IN TWO-DIMENSIONAL BLACK HOLE BACKGROUNDS

Modern Physics Letters A ◽

10.1142/s0217732393001069 ◽

1993 ◽

Vol 08 (14) ◽

pp. 1331-1341 ◽

Cited By ~ 8

Author(s):

SUMIT R. DAS

Keyword(s):

Black Hole ◽

Wave Function ◽

String Theory ◽

Matrix Models ◽

Matrix Model ◽

Asymptotic Region ◽

Two Dimensional ◽

White Hole ◽

Dimensional Black Hole ◽

String Propagation

We identify a quantity in the c = 1 matrix model which describes the wave function for physical scattering of a tachyon from a black hole of the two-dimensional critical string theory. At the semiclassical level this quantity corresponds to the usual picture of a wave coming in from infinity, part of which enters the black hole becoming singular at the singularity, while the rest is scattered back to infinity, with nothing emerging from the white hole. We find, however, that the exact non-perturbative wave function is non-singular at the singularity and appears to end up in the asymptotic region "behind" the singularity.

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