Scientific article
Open access

Peacock patterns and new integer invariants in topological string theory

Published inSciPost physics, vol. 12, no. 2, 058
Publication date2022-02-11
First online date2022-02-11

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.

  • String model: topological
  • Calabi-Yau
  • Spectral
  • Conifold
  • Chern-Simons term
  • Holomorphic
  • Singularity
  • Structure
  • European Commission - Recursive and Exact New Quantum Theory [810573]
Citation (ISO format)
GU, Jie, MARINO BEIRAS, Marcos. Peacock patterns and new integer invariants in topological string theory. In: SciPost physics, 2022, vol. 12, n° 2, p. 058. doi: 10.21468/scipostphys.12.2.058
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Article (Published version)
ISSN of the journal2542-4653

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