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

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.

20 pages RevTeX, 7 figures; v2: matches published version, discussion of Cooper instability improved

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Cited by in corpus (6)

• Chiral Separation effect in non-homogeneous systems
• Effect of interactions on the topological expression for the chiral separation effect
• Equilibrium Chiral Magnetic Effect: spatial inhomogeneity, finite temperature, interactions
• The masses of vector mesons in holographic QCD at finite chiral chemical potential
• Magneto-conductivity and CME in Dirac semimetals from Keldysh technique in Landau levels basis
• A lattice mean-field study of the phase diagram of interacting parity-breaking Weyl semimetals