Seminar: Nicola Dondi (Bern)

Title: Resurgence of the large-charge expansion

Abstract: In this talk I will discuss the d=3 Wilson-Fisher O(N) CFT in a large-charge sector, where also N is taken to be large. The large-charge expansion of critical exponents of the model turns out to be an asymptotic series with double factorial growth. Resurgent methods can be applied to obtain an unambiguous semi-classical reconstruction of this expansion, containing non-perturbative contributions and allowing extrapolation to small charge regimes. This reconstruction can be alternatively derived from a saddle point expansion of worldline path integrals for free particles moving on spheres. In this picture, non-perturbative corrections in the large-charge expansion are in one-to-one correspondence with (unstable) geodesic paths on the sphere, and Borel ambiguities are related to Morse indexes introduced by negative modes deformations.
Based on https://arxiv.org/pdf/2102.12488.pdf in collaboration with I.Kalogerakis, D.Orlando and S.Reffert.

Download the slides here: https://pandora.infn.it/public/slides-dondi