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 flavour D8 and anti-D8-branes. For any finite value of the radius R of the circle around which the colour D4-branes wrap, a non-local Nambu−Jona-Lasinio (NJL) type short-range interaction couples the flavour branes and anti-branes. We argue that chiral symmetry is broken in this model only above a certain critical value of the 4-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 non-compact version of the non-local NJL model.