Numerical evidence of chiral magnetic effect in lattice gauge theory

TL;DR

The paper investigates the Chiral Magnetic Effect (CME) in quenched SU(2) lattice gauge theory by applying a uniform external magnetic field and analyzing local chirality $ ho_5(x)$ and current $j_b(x)$ using the overlap Dirac operator. It demonstrates that magnetic fields enhance longitudinal currents and chirality fluctuations in both confinement and deconfinement, with local fluctuations of topological charge driving CME and global topological charge playing a minor role. The study connects lattice results to STAR experimental data through a simple fireball model, achieving qualitative agreement for charge asymmetry observables while acknowledging limitations of the quenched approximation and finite volume. Overall, the work provides qualitative evidence for CME arising from local topological fluctuations in hot and cold QCD-like matter and highlights temperature-dependent behavior of CME signatures.

Abstract

The chiral magnetic effect is the generation of electric current of quarks along external magnetic field in the background of topologically nontrivial gluon fields. There is a recent evidence that this effect is observed by the STAR Collaboration in heavy ion collisions at RHIC. In our paper we study qualitative signatures of the chiral magnetic effect using quenched lattice simulations. We find indications that the electric current is indeed enhanced in the direction of the magnetic field both in equilibrium configurations of the quantum gluon fields and in a smooth gluon background with nonzero topological charge. In the confinement phase the magnetic field enhances the local fluctuations of both the electric charge and chiral charge densities. In the deconfinement phase the effects of the magnetic field become smaller, possibly due to thermal screening. Using a simple model of a fireball we obtain a good agreement between our data and experimental results of the STAR Collaboration.

Figures (14)

• Figure 1: (color online). The excess of the density of the electric charge (\ref{['eq:j:B']}) due to the applied magnetic field $qB = 0.7\,\hbox{GeV}^2$ on $14^4$ lattice with the volume $(1.44 \, \hbox{fm})^4$. A typical three dimensional slice of a typical gauge field configuration is shown. The magnetic field is directed vertically from the bottom of the picture to the top. The red regions mark the excess of the positive charges while the blue regions correspond to the negative electric charge density.
• Figure 2: (color online). The same as in Figure (\ref{['fig:j0H2']}) but for $qB = 1.8\,\hbox{GeV}^2$ and for the configuration of non-Abelian gauge field.
• Figure 3: (color online). The expectation value of the chirality squared (\ref{['chirality_sq_def']}), $\rho^2_5$, vs. magnetic field at different lattice parameters (the lattice spacing $a$ and the lattice volume $L^4$), and for different number $M$ of Dirac eigenmodes which were taken to determine the truncated Dirac propagator (\ref{['Dirac_propagator']}) used in (\ref{['four_fermion_vev']}) to calculate (\ref{['chirality_sq_def']}).
• Figure 4: (color online). The expectation values of the chirality squared (\ref{['chirality_sq_def']}) vs. the magnetic field at three different temperatures.
• Figure 5: (color online). The same as in Figure \ref{['fig:rho52']} but for the fluctuations (\ref{['eq:j2:def']}) of the electromagnetic current $j_3$ (\ref{['eq:j:def']}).