Non trivial critical exponents for finite temperature chiral transitions at fixed total fermion number

TL;DR

This paper investigates the finite temperature chiral transition in the Gross-Neveu model at fixed fermion number, revealing non-trivial critical exponents and a conformal field theory description involving a transmutation of fermionic statistics.

Contribution

It demonstrates that the chiral transition can be described by a conformal field theory with non-trivial critical exponents, due to a fermion-boson transmutation, in a model with fixed fermion number.

Findings

Model exhibits non-trivial critical exponents at the transition.

Transition region described by a chiral conformal field theory.

Fermions effectively behave as bosons due to statistics transmutation.

Abstract

We analyze the finite temperature chiral restoration transition of the $(D=d+1)$-dimensional Gross-Neveu model for the case of a large number of flavors and fixed total fermion number. This leads to the study of the model with a nonzero imaginary chemical potential. In this formulation of the theory, we have obtained that, in the transition region, the model is described by a chiral conformal field theory where the concepts of dimensional reduction and universality do apply due to a transmutation of statistics which makes fermions act as if they were bosons, having zero energy. This result should be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.