Gravitational Phase Transitions and the Sine-Gordon Model

TL;DR

This paper analyzes the Sine-Gordon model coupled to 2D gravity, revealing phase transitions through a nonperturbative partition function and proposing a semiclassical interpretation of the transition between frozen and dynamical phases.

Contribution

It provides a nonperturbative expression for the partition function of the coupled model and identifies phase transition signals at genus zero.

Findings

Partition function exhibits singularities indicating phase transitions.

A semiclassical picture describes the transition from frozen to dynamical phases.

The model's behavior suggests new insights into 2D quantum gravity coupled to matter.

Abstract

We consider the Sine-Gordon model coupled to 2D gravity. We find a nonperturbative expression for the partition function as a function of the cosmological constant, the SG mass and the SG coupling constant. At genus zero, the partition function exhibits singularities which are interpreted as signals of phase transitions. A semiclassical picture of one of these transitions is proposed. According to this picture, a phase in which the Sine-Gordon field and the geometry are frozen melts into another phase in which the fields and geometry become dynamical.