We study the fixed point of the three-dimensional NJL model in a double-scaling limit where both the charge Q and the number of fermion flavors N become large with a fixed ratio q=Q/(2N). While a similar analysis has been performed for the bosonic O(N) model, fermionic models pose new challenges. In this work, we systematically explore the CFT spectrum in both the large and small q limits beyond the first few orders, and perform a resurgence analysis. Through this approach, we identify the exponential corrections that relate the convergent small-q expansion to the asymptotic large-q behavior. Our results are suggestive of a geometric interpretation of these results in terms of the worldline of particles moving along the geodesics on the cylinder.
