Ref HAL: hal-03271316_v1
Ref Arxiv: 2106.12006
DOI: 10.1007/s00023-021-01129-x
WoS: 000722791700001
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
1 Citation
Résumé:

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.