String Theory seminar - Giacomo Sberveglieri Seminar

Abstract: In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in 1/N, making the 1/N expansion a natural testing ground for the theory of resurgence. We studied in detail the interplay between resurgent properties and the 1/N expansion in various integrable field theories with renormalons, namely the non-linear sigma model, the principal chiral field and the Gross-Neveu models. We focused on the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with the thermodynamic Bethe ansatz (TBA). In this talk, after an introduction on the nature of perturbative series and having set the key ingredients and tools of our study, I’ll present and discuss the results: they turned out to be different in the three models. While in some examples, the terms in the 1/N expansion can be fully decoded in terms of a resurgent trans-series in the coupling constant, in others each term in the 1/N expansion includes non-perturbative corrections which can not be predicted by a resurgent analysis of the corresponding perturbative series. Notably, in the principal chiral field we found a new, explicit solution for the large N free energy which can be written as the median resummation of a trans-series with infinitely many, analytically computable IR renormalon corrections.