Chiral symmetry breaking and external fields in the Kuperstein-Sonnenschein model

Abstract

A novel holographic model of chiral symmetry breaking has been proposed by Kuperstein and Sonnenschein by embedding non-supersymmetric probe D7 and anti-D7 branes in the Klebanov-Witten background. We study the dynamics of the probe flavours in this model in the presence of finite temperature and a constant electromagnetic field. In keeping with the weakly coupled field theory intuition, we find the magnetic field promotes spontaneous breaking of chiral symmetry whereas the electric field restores it. The former effect is universally known as the "magnetic catalysis" in chiral symmetry breaking. In the presence of an electric field such a condensation is inhibited and a current flows. Thus we are faced with a steady-state situation rather than a system in equilibrium. We conjecture a definition of thermodynamic free energy for this steady-state phase and using this proposal we study the detailed phase structure when both electric and magnetic fields are present in two representative configurations: mutually perpendicular and parallel.