Strong-Weak Duality and Quantum Modularity of Resurgent Topological Strings

par Claudia Rella (Université de Genève)

jeudi 7 mars 2024, 14:30 → 16:00 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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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