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Modularity and resurgence in N=4 supersymmetric Yang-Mills theory

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AR2W03 - Applicable resurgent asymptotics: summary workshop

In this talk I review some new exact results and discuss various open questions in N=4 supersymmetric Yang-Mills theory. For the concrete physical observables I describe, there is a beautiful interplay between their resurgence and modular properties. These quantities are found to satisfy intriguing “Laplace-difference equation” under the action of the hyperbolic Laplace operator with respect to the complex YM coupling. Their perturbative expansions can be reconstructed from infinite series of non-holomorphic Eisenstein series of either integer or half-integer index, while the non-perturbative resurgent terms are expressed in terms of novel non-holomorphic modular functions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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