$U_L(N)\times U_R(N)$-invariant four-fermion interactions and Nambu-Goldstone mechanism at finite temperature

TL;DR

This paper demonstrates that in a finite-temperature chiral fermion model with $U_L(N) imes U_R(N)$ symmetry, the Goldstone theorem holds, producing massive scalars and massless pseudoscalars consistent with thermal field theory.

Contribution

It proves the finite-temperature Goldstone theorem in a specific NJL-type fermion model with $U_L(N) imes U_R(N)$ symmetry, confirming the existence of Nambu-Goldstone bosons.

Findings

At temperatures below $T_c$, the model predicts $N^2$ massive scalars and $N^2$ massless pseudoscalars.

The Goldstone theorem remains valid at finite temperature within the real-time formalism.

The symmetry breaking pattern is $U_L(N) imes U_R(N) o U_{L+R}(N)$.

Abstract

In a chiral $U_L(N)\times U_R(N)$ fermion model of NJL-form, we prove that, if all the fermions are assumed to have equal masses and equal chemical potentials, then at the finite temperature $T$ below the symmetry restoration temperature $T_c$, there will be $N^2$ massive scalar composite particles and $N^2$ massless pseudoscalar composite particles (Nambu-Goldstone bosons). This shows that the Goldstone Theorem at finite temperature for spontaneous symmetry breaking $U_L(N)\times U_R(N) \to U_{L+R}(N)$ is consistent with the real-time formalism of thermal field theory in this model.