Peacock patterns, or how to get integer invariants from perturbative series

Abstract: Quantum field and string theories often lead to perturbative series which encode geometric information. In this talk I will argue that, in the case of complex Chern-Simons theory and topological string theory, these perturbative series secretly encode integer invariants, related in some cases to BPS counting. The framework which makes this relation possible is the theory of resurgence, where perturbative series lead to additional non-perturbative sectors. I’ll show that the integer invariants arise as Stokes constants of the resulting resurgent structure, in what we call a ``peacock pattern”. I will illustrate these claims with explicit examples related to hyperbolic knots and toric Calabi-Yau threefolds. Factorization in (anti)holomorphic blocks and the correspondence between topological strings and spectral theory turn out to play an important role in the story.

HEP - theorymathematical physics

Audience: researchers in the topic

QFT and Geometry

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