Intersecting branes and Nambu$-$Jona-Lasinio model

TL;DR

This paper investigates chiral symmetry breaking in a string theory model involving intersecting branes, demonstrating a critical coupling threshold and exploring the effects of different geometric limits on the phenomenon.

Contribution

It provides a detailed analysis of chiral symmetry breaking at weak coupling in the Sakai-Sugimoto model, including numerical solutions and the impact of geometric parameters.

Findings

Chiral symmetry breaks only above a critical 't Hooft coupling.

Numerical solutions confirm the existence of a phase transition.

Limit R → ∞ does not yield a consistent chiral symmetry breaking picture.

Abstract

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 $R \to \infty$ 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.