Intersecting branes and Nambu-Jona-Lasinio model

We discuss chiral symmetry breaking in the intersecting brane model of Sakai and Sugimoto at weak coupling for a generic value of separation L between the flavor D8 and anti-D8-branes. For any finite value of the radius R of the circle around which the color D4-branes wrap, a nonlocal Nambu-Jona-Lasinio-type short-range interaction couples the flavor branes and antibranes. We argue that chiral symmetry is broken in this model only above a certain critical value of the four-dimensional 't Hooft coupling and confirm this through numerical calculations of solutions to the gap equation. We also numerically investigate chiral symmetry breaking in the limit R→∞ keeping L fixed, but find that simple ways of implementing this limit do not lead to a consistent picture of chiral symmetry breaking in the noncompact version of the nonlocal Nambu-Jona-Lasinio model.