Comments on Critical Electric and Magnetic Fields from Holography

TL;DR

This paper explores the critical electric and magnetic fields in holographic dual theories, analyzing instabilities, pair production mechanisms, and effects of combined fields and finite temperature, extending previous work on electric fields.

Contribution

It extends the analysis of critical electric fields to magnetic fields in holography, examining monopole pair production and combined E-B effects at finite temperature.

Findings

Magnetic fields are stable against perturbative instabilities at large coupling.

Critical magnetic fields induce monopole pair production via tunneling.

Finite temperature modifies Schwinger critical phenomena.

Abstract

We discuss some aspects of critical electric and magnetic fields in a field theory with holographic dual description. We extend the analysis of arxiv:1109.2920, which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields. We first find that, unlike ordinary weakly coupled theories, the magnetic field is not subject to any perturbative instability originating from the presence of a tachyonic ground state in the W-boson spectrum. This follows from the large value of the 't Hooft coupling \lambda, which prevents the Zeeman interaction term to overcome the particle mass at high B. Consequently, we study the next possible B-field instability, i.e. monopole pair production, which is the S-dual version of the Schwinger effect. Also in this case a critical magnetic field is expected when the tunneling barrier drops to zero. These Schwinger-type criticalities are the holographic duals, in the bulk, to the fields E or B reaching the tension of F1 or D1 strings respectively. We then discuss how this effect is modified when electric and magnetic fields are present simultaneously and dyonic states in the spectrum can be pair produced by a generic E - B background. Finally, we analyze finite temperature effects on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.