Marginal perturbative series of integrable critical XXX spin chain: renormalon, resurgence and power corrections

by Yizhuang Liu (Jagiellonian University, Cracow)

Monday 12 Feb 2024, 13:00 → 14:00 Europe/Budapest

Tanác (III. ép.)

In this talk, I present our recent work on perturbative/trans-series of integrable critical XXX antiferromagnetic spin chains with arbitrary spin s, for the ground state energy in the small external field limit.  By applying Wiener-Hopf analysis to thermodynamic Bethe ansatz (TBA) equations, we generated in a systematic way the perturbative series in natural running coupling constants, obtained their singularity structures in the Borel plane, and revealed the conspiracy between the Borel singularities and non-perturbative exponentially small contributions (eg, resurgence structure). It turns out that the perturbative series relates to that for a class of massive integrable deformations of  SU(2) WZW CFT at level 2s by sign flip in the coupling constants. Moreover, for s>1, the leading singularities in the Borel plane are located at t=k/s (k>=1), and they conspire with fractional power-corrections at h^{2+k/s}. In the large s limit, such fractional power corrections condense into a new branch cut and the perturbative series in this limit is controlled by the O(4) non-linear sigma model's integral kernel.