Theoretical Physics Seminar: Resurgence and Asymptotics in AdS/CFT

by Dr Ines Aniceto (Institute of Physics, Jagiellonian University, Kraków, Poland)

Wednesday 17 May 2017, 15:00 → 16:00 Europe/Rome

Aula Teorici (Dipartimento di Fisica e Astronomia)

In order to study the weakly coupled regime of some given quantum theory we often make use of perturbative expansions of the physical quantities of interest. But such expansions are often divergent, and defined only as asymptotic series. This divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects not captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. Moreover, it allows us to construct a full non-perturbative solution from perturbative data. In this talk, I will review the essential role of resurgence theory in the description of the analytic solution behind the asymptotic series. I will further present some major applications of this construction in the context of AdS/CFT. The first of these is the cusp anomalous dimension in $\mathcal{N}=4$ SYM, whose asymptotic expansion at large coupling is resurgent and can be resumed to perform a strong/weak coupling interpolation, connecting to well known results at weak coupling. The second example is a toy example of hydrodynamic theories mimicking the existence of black brane quasinormal modes appearing on the gravity dual description of a $\mathcal{N}=4$ SYM plasma. I will finalise with the mention of novel results in the large-N resurgent dynamics of certain matrix models.