Sine-Gordon Field Theory for the Kosterlitz-Thouless Transitions on Fluctuating Membranes

TL;DR

This paper extends the sine-Gordon model to describe Kosterlitz-Thouless transitions on fluctuating membranes, incorporating curvature effects and deriving renormalization-group relations using field theory techniques.

Contribution

It introduces a sine-Gordon Hamiltonian with curvature couplings for membranes and derives RG equations for this extended model.

Findings

Curvature couplings modify the sine-Gordon Hamiltonian.

Renormalization-group equations are derived for the membrane case.

The model provides insights into phase transitions on fluctuating surfaces.

Abstract

In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians to describe the Kosterlitz-Thouless transition on a fluctuating surface. These Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat surface. In this paper, we derive renormalization-group recursion relations for the sine-Gordon model using field-theoretic techniques developed to study flat space problems.