Peacock patterns and new integer invariants in topological string theory

Abstract

Topological string theory near the conifold point of a Calabi-Yau threefold gives rise to factorially divergent power series which encode the all-genus enumerative information. These series lead to infinite towers of singularities in their Borel plane (also known as "peacock patterns"), and we conjecture that the corresponding Stokes constants are integer invariants of the Calabi-Yau threefold. We calculate these Stokes constants in some toric examples, confirming our conjecture and providing in some cases explicit generating functions for the new integer invariants, in the form of q-series. Our calculations in the toric case rely on the TS/ST correspondence, which promotes the asymptotic series near the conifold point to spectral traces of operators, and makes it easier to identify the Stokes data. The resulting mathematical structure turns out to be very similar to the one of complex Chern-Simons theory. In particular, spectral traces correspond to state integral invariants and factorize in holomorphic/anti-holomorphic blocks.

51 pages, 11 figures, typos corrected, new clarification added

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• Black Hole Entropy, Quantum Corrections and EFT Transitions
• Exact instanton transseries for quantum mechanics
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Large N instantons from topological strings
• Resurgence of Refined Topological Strings and Dual Partition Functions
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Resurgence in complex Chern-Simons theory at generic levels
• Modular resurgence, $q$-Pochhammer symbols, and quantum operators from mirror curves
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions