Numerical Study of Nonperturbative Corrections to the Chiral Separation Effect in Quenched Finite-Density QCD

Abstract

We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

Chiral separation effect in lattice regularization

“…This is because then the limit N t → ∞ means the transition to continuum limit, and the appropriate tuning of the lattice spacing a allows to treat the final answer as the axial current at finite temperature T = 1/(N t a). However, for the interacting system the situation may be different, and at finite temperatures the corrections to the CSE current may appear [40] -the effect, which we do not discuss here.…”

Chiral separation effect for spin 3/2 fermions

“…Firstly, the effect exists in thermodynamic equilibrium -the resulting current is nondissipative. Though the original derivation [1] employed subtractions of non-renormalized quantities, 2 analytical studies [2] in a well-regularized theory and numerical studies [3] confirmed the result.…”

The Chiral Separation Effect in quenched finite-density QCD

“…The plots in Figure 3 clearly show that for the larger lattice volume the data for all topological sectors and chemical potentials we investigated are in perfect agreement with the free fermion result σ 0 CSE . A possible reason for the large finite size effects in topological sectors with non-zero Q is discussed in [32]. The results for all our simulations on larger lattices are summarised in Figure 2a. …”

“…In this contribution we report on a first-principles lattice study of the CSE, previously published in [32]. To avoid unquantifiable systematic errors we work with finite-density overlap fermions [33], which respect a lattice version of chiral symmetry, and use the properly defined conserved lattice axial vector current density [34,35]:…”