Chiral symmetry breaking and pions in nonsupersymmetric gauge/gravity duals

Abstract

We study gravity duals of large N nonsupersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a nonconstant dilaton and ${S}^{5}$ radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the $\overline{\ensuremath{\Psi}}\ensuremath{\Psi}$ condensate and meson spectrum associated with these backgrounds. In the AdS--black-hole background, a quark-bilinear condensate develops only at a nonzero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.