Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions

TL;DR

This paper calculates how finite temperature affects the induced fermion number in a (2+1)-dimensional nonlinear sigma model, revealing temperature-dependent, non-topological corrections that depend on the background shape.

Contribution

It provides the first detailed analysis of finite temperature effects on fermion number in this model, including all-order resummation at low temperatures and explicit background examples.

Findings

Finite temperature introduces non-topological corrections to fermion number.

Resummation of the derivative expansion is performed at low temperature.

Explicit background solutions like CP^1 instantons and baby skyrmions are analyzed.

Abstract

We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in (2+1) dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological -- this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a CP^1 instanton or as a baby skyrmion.