Overlap Dirac operator with chiral chemical potential and Chiral Magnetic Effect on the lattice

TL;DR

This paper develops a lattice Dirac operator with chiral chemical potential to study the Chiral Magnetic Effect, revealing discrepancies with anomaly-based predictions due to infrared sensitivities in lattice calculations.

Contribution

It introduces a self-consistent overlap lattice Dirac operator with chiral chemical potential and analyzes its implications for the Chiral Magnetic Effect on the lattice.

Findings

Discrepancy between lattice results and anomaly-based predictions.

Infrared singularities influence lattice calculations of the CME.

Finite volume and temperature affect the results significantly.

Abstract

A self-consistent construction of the overlap lattice Dirac operator coupled to chiral chemical potential is proposed. With the help of the constructed operator we compute electric current induced by a constant magnetic field (Chiral Magnetic Effect). We find that the result disagrees with the one predicted by anomaly-based arguments and comment on the origin of this discrepancy. We demonstrate that a straightforward lattice calculation with a constant magnetic field and a uniform chiral chemical potential in fact corresponds to an infrared singularity in the dimensionally reduced polarization tensor and hence yields the result which is extremely sensitive to infrared regulators such as finite volume or finite temperature.