  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.
