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

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.

Figure 1

Axial current density as a function of the magnetic field strength for topological charge $Q=0$ (red circles with error bars) at $T>T_c$ (left) and $T<T_c$ (right). Black lines correspond to the free fermion result ${\sigma }_{\mathrm{CSE}}^0$ for both values of the chemical potential. The shaded regions mark the confidence intervals (CI) for ${\sigma }_{\mathrm{CSE}}$ with different numbers of stochastic estimators.

Figure 2

Confidence intervals for the ratio ${\sigma }_{\mathrm{CSE}}/{\sigma }_{\mathrm{CSE}}^0$ for different values of the chemical potential and the topological charge. Boxes and whiskers mark the confidence interval for a fit with all data points and with the largest value of ${\mathrm{\Phi }}_B$ excluded, respectively. Filled and open boxes are the results for $T<T_c$ and $T>T_c$, respectively.

Figure 3

The axial current in different topological sectors. Filled symbols mark the results for $m_q=0.001a^{-1}$; the results for $m_q=0.002a^{-1}$ are shifted by $0.02a^{-2}$ in the $qB$ axis for better visibility and are marked by open symbols. The black dots denote the axial current with $Q=0$ for vanishing quark mass, and the black dashed line corresponds to the free fermion result ${\sigma }_{\mathrm{CSE}}^0$. To guide the eye a linear ($Q=0$) or second order polynomial ($|Q|>0$) fit to the data is shown. For comparison, we also plot the results for $|Q|>0$ for the $14\times 14^3$ lattice.