Holographic Schwinger Effect and Chiral condensate in SYM Theory

TL;DR

This paper investigates the Schwinger effect and chiral condensate in supersymmetric Yang-Mills theories using holographic methods, analyzing quark pair production rates across different phases and estimating the dynamical quark mass.

Contribution

It provides a holographic calculation of the Schwinger effect in ${ m extbf{N}=2}$ SYM theory and extends the analysis to finite temperature phases, linking pair production to chiral condensate behavior.

Findings

Calculated quark pair production rates in various phases.

Estimated dynamical quark mass from production rates.

Suggested extension of Nambu-Jona-Lasinio model to finite temperature YM theory.

Abstract

We study the instability, for the supersymmetric Yang-Mills (SYM) theories, caused by the external electric field through the imaginary part of the action of the D7 probe brane, which is embedded in the background of type IIB theory. This instability is related to the Schwinger effect, namely to the quark pair production due to the external electric field, for the $SU(N_c)$ SYM theories. In this holographic approach, it is possible to calculate the Schwinger effect for various phases of the theories. Here we give the calculation for ${\cal N}=2$ SYM theory and the analysis is extended to the finite temperature deconfinement and the zero temperature confinement phases of the Yang-Mills (YM) theory. By comparing the obtained production rates with the one of the supersymmetric case, the dynamical quark mass is estimated and we find how it varies with the chiral condensate. Based on this analysis, we give a speculation on the extension of the Nambu-Jona-Lasinio model to the finite temperature YM theory, and four fermi coupling is evaluated in the confinement theory.