Chiral symmetry breaking from two-loop effective potential of the holographic non-local NJL model

TL;DR

This paper computes the two-loop effective potential of a holographic non-local NJL model derived from string theory, confirming that chiral symmetry breaking persists at weak coupling beyond one-loop analysis.

Contribution

It provides the first two-loop calculation of the effective potential in the holographic non-local NJL model, extending understanding of chiral symmetry breaking at weak coupling.

Findings

Two-loop potential is negative for both symmetric and broken vacua.

Chiral symmetry breaking remains at weak coupling at two-loop level.

Two-loop effects reinforce the persistence of chiral symmetry breaking.

Abstract

We calculate the two-loop effective potential of the non-local NJL model derived from the Sakai-Sugimoto model in string theory. In contrast to conventional NJL with 4-fermion contact interaction, the chiral symmetry was previously found to be dynamically broken for arbitrary weak coupling at the one-loop level. As a confirmation, the approximate numerical solutions to the gap equation at one loop are explicitly demonstrated for weak couplings. We then calculate the one and two-loop contribution to the effective potential of the non-local NJL model and found that the two-loop contribution is negative. The two-loop potential for the chiral symmetric vacuum is also negative but larger than the combined effective potential of the chiral broken vacuum at the two-loop level. The chiral symmetry breaking thus persists for arbitrary weak coupling at the two-loop level.