Spontaneous chiral symmetry breaking and the Chiral Magnetic Effect for interacting Dirac fermions with chiral imbalance

TL;DR

This study investigates how chiral imbalance influences spontaneous chiral symmetry breaking and the chiral magnetic effect in interacting Dirac fermions, revealing phase transitions, conductivity behavior, and meson mixing patterns relevant to Weyl semimetals and QCD.

Contribution

It provides a mean-field analysis of chiral symmetry breaking with chiral imbalance, highlighting effects on vacuum energy, phase transition characteristics, and magnetic conductivity in Dirac fermion systems.

Findings

Chiral imbalance lowers vacuum energy and increases chiral chemical potential.

Critical coupling for symmetry breaking decreases with chiral imbalance.

Chiral magnetic conductivity increases in both weak and strong coupling regimes.

Abstract

We report on a mean-field study of spontaneous breaking of chiral symmetry for Dirac fermions with contact interactions in the presence of chiral imbalance, which is modelled by nonzero chiral chemical potential. We point out that chiral imbalance lowers the vacuum energy of Dirac fermions, which leads to the increase of the renormalized chiral chemical potential upon chiral symmetry breaking. The critical coupling strength for the transition to the broken phase is slightly lowered as the chiral chemical potential is increased, and the transition itself becomes milder. Furthermore, we study the chiral magnetic conductivity in different phases and find that it grows both in the perturbative weak-coupling regime and in the strongly coupled phase with broken chiral symmetry. In the strong coupling regime the chiral magnetic effect is saturated by vector-like bound states (vector mesons) with mixed transverse polarizations. General pattern of meson mixing in the presence of chiral imbalance is also considered. We discuss the relevance of our study for Weyl semimetals and strongly interacting QCD matter. Finally, we comment on the ambiguity of the regularization of the vacuum energy of Dirac fermions in the presence of chirality imbalance.