For the 3d NJL model at large charge, the scaling dimension has a convergent small-q series and an asymptotic large-q series whose nonperturbative corrections are worldline-instanton terms e^{-α√q}.
In particular, the free bosonic and fermionic path integrals are normalized to 1√ 4πt and unity, respectively
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Resurgence Analysis of the Nambu-Jona-Lasinio model at large charge
For the 3d NJL model at large charge, the scaling dimension has a convergent small-q series and an asymptotic large-q series whose nonperturbative corrections are worldline-instanton terms e^{-α√q}.