The Gravitational Sine-Gordon Model

TL;DR

This paper investigates the Sine-Gordon model coupled to 2D gravity using matrix models, showing the flow from a $c=1$ string in the UV to decoupled $c=0$ models in the IR, and demonstrating the monotonic decrease of the torus partition sum.

Contribution

It provides a matrix model analysis of the gravitational Sine-Gordon model, revealing the RG flow from $c=1$ to $c=0$ and confirming the $c$-theorem via the torus partition sum.

Findings

The $c=1$ string flows to decoupled $c=0$ models in the IR.

The torus partition sum decreases monotonically with scale.

The model supports a $c$-theorem in 2D quantum gravity.

Abstract

We use matrix model results to investigate the Sine-Gordon model coupled to two dimensional gravity. For relevant (in the RG sense) potentials, we show that the $c=1$ string, which appears in the ultraviolet limit of this model, flows to a set of decoupled $c=0$ (pure gravity) models in the infrared. The torus partition sum, which was argued previously to count the number of string degrees of freedom and hence satisfy a new $c$ -- theorem, is shown to be a monotonically decreasing function of the scale (given by the quantum area of the world-sheet).