# Conformal TBA for resolved conifolds

Abstract : We revisit the Riemann-Hilbert problem determined by Donaldson-Thomas invariants for the resolved conifold and for other small crepant resolutions. While this problem can be recast as a system of TBA-type equations in the conformal limit, solutions are ill-defined due to divergences in the sum over infinite trajectories in the spectrum of D2-D0-brane bound states. We explore various prescriptions to make the sum well-defined, show that one of them reproduces the existing solution in the literature, and identify an alternative solution which is better behaved in a certain limit. Furthermore, we show that a suitable asymptotic expansion of the $\tau$ function reproduces the genus expansion of the topological string partition function for any small crepant resolution. As a by-product, we conjecture a new integral representation for the double sine function.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03271316
Contributor : L2c Aigle <>
Submitted on : Friday, June 25, 2021 - 3:45:27 PM
Last modification on : Tuesday, July 13, 2021 - 3:26:42 AM

### Identifiers

• HAL Id : hal-03271316, version 1
• ARXIV : 2106.12006

### Citation

Sergey Alexandrov, Boris Pioline. Conformal TBA for resolved conifolds. 2021. ⟨hal-03271316⟩

Record views