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.

18/07/2016, 11:30 — 12:30 — Amphitheatre Ea1, North Tower, IST
Jorge Russo, University of Barcelona

Supersymmetric Gauge Theories and Resurgence

We discuss supersymmetric observables in four-dimensional ${\mathcal N}=2$ gauge theories. Some of them are given in terms of closed, analytic formulas, which exhibit the explicit dependence on couplings, masses and on the rank $N_c$ of the gauge group. We comment on some features of the $1/N_c$ expansion and of the weak coupling expansion. We also discuss some salient aspects of SQCD with two massive flavors, and of ${\mathcal N}=2$ gauge theory on ellipsoids.

See also

R-russo.pdf

18/07/2016, 10:00 — 11:00 — Amphitheatre Ea1, North Tower, IST
Michael Berry, Bristol University

Two Physical Applications of Divergent Series: The Aharonov-Bohm Wave, and Exquisite Sensitivity of Optical Polarization

1. Approximate connections between the Aharonov-Bohm wave (AB) scattered by a magnetic flux line and the Fresnel-Sommerfeld edge-diffracted wave have been known for decades. The connection can be made precise by representing AB as a series whose large parameter is distance from the flux; the Erf-based approximation is uniform in angle and flux. The series diverges, and can be resummed to give additional accuracy, even within one wavelength of the flux.
2. Divergent series and nonhermitian degeneracies combine in the optics of polarized light traversing a slowly-twisted anisotropic absorbing material, leading to a prediction that the emergent polarization is extraordinarily sensitive to the incident polarization - a dramatic violation of adiabatic intuition, explained by the Stokes phenomenon.