Quark mass in the Sakai-Sugimoto model of chiral symmetry breaking

We re-analyze D8 brane embeddings in the geometry of a D4 brane wrapped on a circle that describe chiral symmetry breaking in a strongly coupled non-supersymmetric gauge theory. We argue that if the holographic fields are correctly interpreted, the original embeddings describe a complex quark mass and condensate in the theory. We show that in this interpretation when a quark mass is present there is a massive pseudo Goldstone boson (pion). A previously identified massless fluctuation is, we argue, not a physical state in the field theory. We also determine the behaviour of the quark condensate as a function of the quark mass