Euler-Heisenberg-Weiss action for QCD+QED

TL;DR

This paper derives an analytic one-loop effective action for QCD+QED at various temperatures, unifying electromagnetic, chromo-electromagnetic fields, and the Polyakov loop, with applications to quark pair production and the Polyakov loop behavior under strong fields.

Contribution

It introduces the Euler-Heisenberg-Weiss action for QCD+QED, extending previous actions to include finite temperature effects and the Polyakov loop, providing a new tool for analyzing strong field phenomena.

Findings

Quark pair production is influenced by combined QCD+QED fields.

The effective potential of the Polyakov loop is explicitly affected by magnetic fields.

Magnetic fields enhance the breaking of center symmetry, consistent with inverse magnetic catalysis.

Abstract

We derive an analytic expression for one-loop effective action of QCD+QED at zero and finite temperatures by using the Schwinger's proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED+QCD, and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD+QED, we investigate quark pair productions induced by QCD+QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.