Exact Effective Action for (1+1 Dimensional) Fermions in an Abelian Background at Finite Temperature

TL;DR

This paper derives an exact, non-analytic effective action for 1+1 dimensional fermions in an Abelian background at finite temperature, revealing interactions at all orders without quantum corrections, with potential applications to higher-dimensional models.

Contribution

It provides the first exact finite-temperature effective action for 1+1D fermions in an Abelian gauge field, showing all-order interactions and non-analytic structure.

Findings

Effective action is non-analytic at finite temperature.

Interactions occur at all even orders without quantum corrections.

Results may aid in studying 2+1D models and finite-temperature solvability.

Abstract

In an effort to further understand the structure of effective actions for fermions in an external gauge background at finite temperature, we study the example of 1+1 dimensional fermions interacting with an arbitrary Abelian gauge field. We evaluate the effective action exactly at finite temperature. This effective action is non-analytic as is expected at finite temperature. However, contrary to the structure at zero temperature and contrary to naive expectations, the effective action at finite temperature has interactions to all (even) orders (which, however, do not lead to any quantum corrections). The covariant structure thus obtained may prove useful in studying 2+1 dimensional models in arbitrary backgrounds. We also comment briefly on the solubility of various 1+1 dimensional models at finite temperature.