The Annular Report on Non-Critical String Theory

TL;DR

This paper explores the application of annulus partition functions in Liouville field theory to non-critical string theory, establishing connections with matrix models, D-branes, and two-dimensional de Sitter gravity across different dimensions.

Contribution

It demonstrates the precise reproduction of matrix model results from worldsheet formulations and links eigenvalue instantons to disk instantons, revealing D-branes as effective dynamics in non-critical string theory.

Findings

Reproduces matrix model correlation functions using worldsheet methods.

Identifies eigenvalue instantons with disk instantons, linking matrix and worldsheet approaches.

Models two-dimensional de Sitter gravity via Liouville theory with D-brane boundary conditions.

Abstract

Recent results on the annulus partition function in Liouville field theory are applied to non-critical string theory, both below and above the critical dimension. Liouville gravity coupled to $c\le 1$ matter has a dual formulation as a matrix model. Two well-known matrix model results are reproduced precisely using the worldsheet formulation: (1) the correlation function of two macroscopic loops, and (2) the leading non-perturbative effects. The latter identifies the eigenvalue instanton amplitudes of the matrix approach with disk instantons of the worldsheet approach, thus demonstrating that the matrix model is the effective dynamics of a D-brane realization of $d\le 1$ non-critical string theory. In the context of string theory above the critical dimension, i.e. $d\ge 25$, Liouville field theory realizes two-dimensional de Sitter gravity on the worldsheet. In this case, appropriate D-brane boundary conditions on the annulus realize the S-matrix for two-dimensional de Sitter gravity.