Holographic Nambu Jona-Lasinio Interactions

TL;DR

This paper explores how Nambu Jona-Lasinio (NJL) interactions influence chiral symmetry breaking in a holographic D3/D7 system, revealing conditions under which NJL induces or enhances chiral condensation, including effects at finite temperature and magnetic fields.

Contribution

It introduces NJL interactions into a holographic D3/D7 setup using double trace operators and analyzes their impact on chiral symmetry breaking under various conditions.

Findings

NJL interactions do not induce chiral symmetry breaking in supersymmetric systems.

Chiral condensation can be triggered by NJL interactions at a second order transition with an IR cutoff.

Finite temperature and magnetic fields modify the phase transition behavior, including first order transitions.

Abstract

NJL interactions are introduced into the D3/ probe D7 system using Witten's double trace operator prescription which includes the operator as a classical term in the effective potential. In the supersymmetric system they do not induce chiral symmetry breaking which we attribute to the flat effective potential with quark mass in the supersymmetric theory. If additional supersymmetry breaking is introduced then standard NJL behaviour is realized. In examples where chiral symmetry breaking is not preferred such as with a B field plus an IR cut off chiral condensation is triggered by the NJL interaction at a second order transition after a finite critical coupling. If the model already contains chiral symmetry breaking, for example in the B field case with no IR cut off, then the NJL interaction enhances the quark mass at all values of the NJL coupling. We also consider the system at finite temperature: the temperature discourages condensation but when combined with a magnetic field we find regions of parameter space where the NJL interaction triggers a first order chiral transition above a critical coupling.