Non-Perturbative Effects in Matrix Models and D-branes

TL;DR

This paper investigates non-perturbative effects in matrix models and their relation to D-branes in Liouville theory, demonstrating agreement between continuum and matrix model approaches in various conformal field theories.

Contribution

It establishes a detailed correspondence between non-perturbative effects in matrix models and localized D-branes in Liouville theory across multiple CFT cases.

Findings

Agreement between matrix model predictions and Liouville theory results.

Derivation of properties of D-branes near the tip of the cigar in SL(2)/U(1) CFT.

Insights into non-perturbative effects in c≤1 string theories.

Abstract

The large order growth of string perturbation theory in $c\le 1$ conformal field theory coupled to world sheet gravity implies the presence of $O(e^{-{1\over g_s}})$ non-perturbative effects, whose leading behavior can be calculated in the matrix model approach. Recently it was proposed that the same effects should be reproduced by studying certain localized D-branes in Liouville Field Theory, which were constructed by A. and Al. Zamolodchikov. We discuss this correspondence in a number of different cases: unitary minimal models coupled to Liouville, where we compare the continuum analysis to the matrix model results of Eynard and Zinn-Justin, and compact c=1 CFT coupled to Liouville in the presence of a condensate of winding modes, where we derive the matrix model prediction and compare it to Liouville theory. In both cases we find agreement between the two approaches. The c=1 analysis also leads to predictions about properties of D-branes localized in the vicinity of the tip of the cigar in SL(2)/U(1) CFT with c=26.