Chiral Magnetic Effect and Negative Magnetoresistance across the phase diagram of finite-density SU(2) gauge theory

TL;DR

This study investigates the Chiral Magnetic Effect and Negative Magnetoresistance in SU(2) gauge theory at finite temperature and density, revealing their behaviors across different phases and challenging some theoretical expectations.

Contribution

It provides the first lattice-based analysis of CME and NMR responses in SU(2) gauge theory at finite density and temperature, highlighting their weak dependence on these parameters.

Findings

CME response is close to free quark predictions in the quark-gluon plasma phase.

NMR is strongly suppressed at high densities or temperatures.

The relation between CME and NMR is not straightforward at small magnetic fields.

Abstract

We study the signatures of the Chiral Magnetic Effect (CME) in $SU(2)$ gauge theory with $N_f = 2$ flavours of dynamical fermions at finite temperature $T$, quark chemical potential $\mu$ and a weak external magnetic field $e B$. We consider both the correlator of the axial density and the vector current, which gives direct access to the out-of-equilibrium CME, and the correlator of two vector currents, which probes the CME indirectly via the enhancement of the longitudinal electric conductivity (Negative Magnetoresistance, NMR). We find that the CME response extracted from the vector-axial correlator exhibits a rather weak dependence on temperature and density in the quark-gluon plasma regime, and is very close to the universal value for free massless quarks. The CME is mildly suppressed at low temperatures and large densities in the hadronic phase. In contrast, the NMR behaves in a qualitatively different way across the phase diagram, and is strongly suppressed at either large densities or temperatures. The magnitude of the NMR response appears to be considerably smaller than the prediction based on the lowest Landau level calculation for free quarks. Our findings suggest that for relatively small magnetic field strengths $e B \lesssim m_{\pi}^2$ the relation between the CME and NMR might not be as direct as expected. We also do not find statistically significant indications for an enhancement of the CME strength in the vicinity of the crossover or second-order phase transition lines in the $(\mu, T)$ phase diagram.