The Kosterlitz-Thouless Phenomenon on a Fluid Random Surface

TL;DR

This paper investigates the Kosterlitz-Thouless transition on a fluid random surface incorporating vortices, using a random matrix approach to derive an exact partition function and analyze phase behavior under 2D quantum gravity.

Contribution

It provides an exact solution for the partition function of a scalar field with vortices on a dynamical random lattice, connecting the Kosterlitz-Thouless transition with 2D quantum gravity.

Findings

Exact partition function at a specific radius in the plasma phase

Description of the KT transition in the presence of 2D quantum gravity

Insights into phase transition behavior on dynamical random surfaces

Abstract

The problem of a periodic scalar field on a two-dimensional dynamical random lattice is studied with the inclusion of vortices in the action. Using a random matrix formulation, in the continuum limit for genus zero surfaces the partition function is found exactly, as a function of the chemical potential for vortices of unit winding number, at a specific radius in the plasma phase. This solution is used to describe the Kosterlitz- Thouless phenomenon in the presence of 2D quantum gravity as one passes from the ultra-violet to the infra-red.