Séminaire de Mathématique

Strong-Weak Duality and Quantum Modularity of Resurgent Topological Strings

by Claudia Rella (Université de Genève)

Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane


Le Bois Marie 35, route de Chartres CS 40001 91893 Bures-sur-Yvette Cedex

Seminar on Quantum Modularity and Resurgence

Quantizing the mirror curve of a toric Calabi-Yau threefold gives rise to quantum-mechanical operators. Their fermionic spectral traces produce factorially divergent power series in the Planck constant and its inverse, which are conjecturally captured by the Nekrasov-Shatashvili and standard topological strings via the TS/ST correspondence. In this talk, I will discuss a general conjecture on the resurgence of these dual asymptotic series, and I will present a proven exact solution in the case of the first spectral trace of local $P^2$. A remarkable number-theoretic structure underpins the resurgent properties of the weak and strong coupling expansions and paves the way for new insights relating them to quantum modular forms. Finally, I will mention how these results fit into a broader paradigm linking resurgence and quantum modularity. This talk is based on arXiv:2212.10606 and further work with V. Fantini (available soon).


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Organized by

Veronica Fantini & Campbell Wheeler