Holographic Nambu Jona-Lasinio Interactions

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.