Transport coefficients and analytic continuation in dual (1+1)-dimensional models at finite temperature

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 and to the link with integrable field theories. The resummation implicit in duality provides a powerful alternative to the standard diagrammatic evaluation of transport coefficients at finite temperature.