Speaker: Ramon Miravitllas Mas (University of Geneva)

Title: Structure of trans-series in quantum field theory

Date: 13 January 2023, 13 p.m.

Place: Building 3, Meeting room


Perturbative series in quantum field theory are factorially divergent and must be completed with exponentially small corrections in the coupling, which also come with their own factorially divergent series. The object that incorporates the perturbative series plus all exponential corrections is known as trans-series. After Borel summing all the divergent series into a convergent result, one still has to sum over the exponentially small parameter of the trans-series, and the convergence of this sum must also be analyzed. In this talk, I will review what is known about the convergence of the trans-series in quantum field theories, by considering general phenomenological arguments. Then I will compare these general expectations with a concrete example in integrable quantum field theories, where we can analytically compute the trans-series of a special quantity, the free energy, from the Bethe ansatz equations.