Resurgence Analysis of the Nambu-Jona-Lasinio model at large charge

TL;DR

This paper investigates the large charge behavior of the three-dimensional Nambu-Jona-Lasinio model, analyzing its conformal spectrum and resurgence properties to understand the transition from small to large charge regimes.

Contribution

It provides a systematic exploration of the fermionic NJL model's spectrum at large and small charge ratios, including a resurgence analysis linking different expansion regimes.

Findings

Identified exponential corrections connecting small and large charge expansions.

Performed a resurgence analysis revealing geometric interpretations of the model behavior.

Extended the analysis beyond initial orders to understand the full spectrum.

Abstract

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.