The Thermal Renormalization Group for Fermions, Universality, and the Chiral Phase-Transition

TL;DR

This paper develops a thermal renormalization group approach for fermions in finite temperature field theory, revealing how thermal effects influence fermion decoupling and universality in chiral phase transitions.

Contribution

It introduces a real-time thermal RG framework for fermions and uncovers the role of a thermal mass-like term in fermion decoupling and phase transition behavior.

Findings

Thermal mass-like term is essential for fermion decoupling.

Good agreement with other methods on phase transition results.

Contrasts high-temperature scalar dominance with fermionic behavior.

Abstract

We formulate the thermal renormalization group, an implementation of the Wilsonian RG in the real-time (CTP) formulation of finite temperature field theory, for fermionic fields. Using a model with scalar and fermionic degrees of freedom which should describe the two-flavor chiral phase-transition, we discuss the mechanism behind fermion decoupling and universality at second order transitions. It turns out that an effective mass-like term in the fermion propagator which is due to thermal fluctuations and does not break chiral symmetry is necessary for fermion decoupling to work. This situation is in contrast to the high-temperature limit, where the dominance of scalar over fermionic degrees of freedom is due to the different behavior of the distribution functions. The mass-like contribution is the leading thermal effect in the fermionic sector and is missed if a derivative expansion of the fermionic propagator is performed. We also discuss results on the phase-transition of the model considered where we find good agreement with results from other methods.