c < 1 String from Two Dimensional Black Holes

TL;DR

This paper explores various equivalent descriptions of the c < 1 non-critical string, including topological string models and matrix duals, revealing deep connections between these formulations.

Contribution

It demonstrates the equivalence of the topologically twisted SL(2,R)/U(1) model, Landau-Ginzburg model, and matrix model duals for the c < 1 non-critical string.

Findings

Equivalence between topological SL(2,R)/U(1) model and non-critical string spectra

Reproduction of scattering amplitudes in Landau-Ginzburg model

Discussion of matrix model dual description

Abstract

We study a topological string description of the c < 1 non-critical string whose matter part is defined by the time-like linear dilaton CFT. We show that the topologically twisted N=2 SL(2,R)/U(1) model (or supersymmetric 2D black hole) is equivalent to the c < 1 non-critical string compactified at a specific radius by comparing their physical spectra and correlation functions. We examine another equivalent description in the topological Landau-Ginzburg model and check that it reproduces the same scattering amplitudes. We also discuss its matrix model dual description.