Effect of interactions on the topological expression for the chiral separation effect

TL;DR

This paper proves that the topological expression for the chiral separation effect (CSE) conductivity remains valid in interacting systems with chiral symmetry, with implications for quark-gluon matter and Weyl semimetals.

Contribution

It demonstrates the topological nature of CSE conductivity persists under interactions, extending its applicability to realistic systems like neutron stars and Weyl semimetals.

Findings

CSE conductivity remains topological with interactions if chiral symmetry is preserved.

In quark-gluon matter, the standard CSE conductivity value is predicted at high chemical potential.

Topological expression approaches the quark-gluon plasma phase at high chemical potential and temperature.

Abstract

In the absence of interactions the conductivity of chiral separation effect (CSE) in the system of massless fermions is given by topological expression. Interactions might change the pattern drastically. However, we prove that the CSE conductivity is still given by the topological invariant composed of the Green functions at zero temperature as long as the chiral symmetry is present, and if the renormalized axial current is considered. This allows to predict its appearance with the standard value of conductivity per Dirac fermion $\sigma_{CSE} = \frac{1}{2 \pi^2}$ in quark - gluon matter at $T = 0$ and sufficiently large baryon chemical potential, in the hypothetical phase with restored chiral symmetry and without color superconductivity. This phase may be realized inside the neutron stars. We also argue that the same topological expression for the CSE may be observed in Weyl semimetals, which realize the system of interacting relativistic fermions in solid state systems. In order to estimate the non - perturbative corrections to $\sigma_{CSE}$ within QCD at finite temperatures we apply method of field correlators developed by Yu.A.Simonov. As expected, above the deconfinement crossover the topological expression is approached within the quark - gluon plasma phase, when the quark chemical potential is sufficiently large. However, we observe that this occurs only when quark chemical potential is much larger than the thermal (Debye) mass. This range of parameters appears to be far out of the region accessible at the modern colliders.