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

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.