Transport Coefficients and Analytic Continuation in Dual 1+1 Dimensional Models at Finite Temperature

TL;DR

This paper explores the relationship between fermion gas conductivity and dual boson models in 1+1 dimensions at finite temperature, using duality for resummation and analytic continuation to improve transport coefficient calculations.

Contribution

It introduces a duality-based resummation method for calculating transport coefficients in 1+1 dimensional models at finite temperature, addressing infra-red issues and analytic continuation.

Findings

Duality relates fermion conductivity to boson propagator.

Resummation via duality resolves infra-red problems.

High-temperature expressions for boson self-energy derived.

Abstract

The conductivity of a finite temperature 1+1 dimensional fermion gas described by the massive Thirring model is shown to be related to the retarded propagator of the dual boson sine-Gordon model. Duality provides a natural resummation which resolves infra-red problems, and the boson propagator can be related to the fermion gas at non-zero temperature and chemical potential or density. In addition, at high temperatures, we can apply a dimensional reduction technique to find resummed closed expressions for the boson self-energy and relate them to the fermion conductivity. Particular attention is paid to the discussion of analytic continuation. The resummation implicit in duality provides a powerful alternative to the standard diagrammatic evaluation of transport coefficients at finite temperature.