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Peacock patterns and new integer invariants in topological string theory

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arxiv 2104.07437 v4 pith:S5QDNM6F submitted 2021-04-15 hep-th math-phmath.AGmath.MP

Jie Gu , Marcos Marino This is my paper
classification hep-thmath-phmath.AGmath.MP
keywords invariantsintegerseriesstokestheorycalabi-yauconifoldconjecture
verification ladder T0 review T1 audit T2 compute T3 formal
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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.

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