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Mathematics Department Técnico Técnico

Resurgence Meeting Seminar  RSS

18/07/2016, 14:30 — 15:10 — Amphitheatre Ea1, North Tower, IST
Inês Aniceto, Jagiellonian University

Applications of Resurgence in AdS/CFT

The perturbative study of physical observables often leads to asymptotic expansions, and resurgence has played a major role in understanding the nonperturbative phenomena associated with this asymptotic behaviour. In the context of AdS/CFT correspondence, perturbation theory in different regimes of the coupling and rank of the gauge group can lead to both convergent or asymptotic expansions. In this talk, we review the asymptotic regime of two observables in the context of AdS/CFT, focusing on the case of $\mathcal{N}=4$ SYM. The first of these is the cusp anomalous dimension, whose asymptotic expansion at large coupling can be determined via the so-called BES equation, obtained from the integrable properties of the gauge theory. The transseries solution is shown to be resurgent from large-order checks, and a resummation of this transseries allows us to perform a strong/weak coupling interpolation and connect to the well know results at weak coupling.

The second example covered in this talk is the study of the nonperturbative effects of black brane quasinormal modes appearing on the gravity side of the AdS/CFT description of $\mathcal{N}=4$ SYM plasma. The corresponding asymptotic hydrodynamic gradient expansion in the case of boost-invariant flow can be obtained from an AdS/CFT perspective, and shown to have resurgent properties. From the study of toy examples of hydrodynamic theories mimicking the existence of these quasinormal modes, one can write a transseries solution, and use resurgence to study its properties in different hydrodynamic regimes.

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