The threefold way to quantum periods: q-WKB periods, TBA and q-Painlevé equations

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• Fabrizio Del Monte (Université de Montréal)
• Tuesday 08 November 2022, 15:00-17:00
• Seminar Room 2, Newton Institute.

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ARA2 - Applicable resurgent asymptotics: towards a universal theory

In this talk I will illustrate a new relation that is emerging between WKB approximation of q-difference equations, q-Painleve’, and a set of TBA equations associated to del Pezzo surfaces. In particular, I will show how this relation can be used to obtain exactly the spectrum of stable states and the partition functions of certain five-dimensional Quantum Field Theories, obtained by M-theory on an appropriate (local) Calabi-Yau threefold. The exactly solvable spectrum turns out to be given by algebraic solutions of q-Painleve’ equations, and in the corresponding (nonsingular) region in moduli space the Voros symbols turn out to be classically exact.

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

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