RHIND seminar on Mathematical Physics and String Theory

May 2, 2022 at 4 p.m. c.t. only via ZoomIlka Brunner (LMU München)

Nils Carqueville (Universität Wien)

Hans Jockers (JGU Mainz)

Peter Mayr (LMU München)

Simone Noja (Universität Heidelberg)

Ivo Sachs (LMU München)

Johannes Walcher (Universität Heidelberg)

Joint seminar series on Mathematical Physics and String Theory

Murad Alim (Hamburg U.)

BPS invariants of certain physical theories correspond to Donaldson-Thomas (DT) invariants of an associated Calabi-Yau geometry. BPS structures refer to the data of the DT invariants together with their wall-crossing structure. On the same Calabi-Yau geometry another set of invariants are the Gromov-Witten (GW) invariants. These are organized in the GW potential, which is an asymptotic series in a formal parameter and can be obtained from topological string theory. A further asymptotic series in two parameters is obtained from refined topological string theory which contains the Nekrasov-Shatashvili (NS) limit when one of the two parameters is sent to zero. I will discuss in the case of the resolved conifold how all these asymptotic series lead to difference equations which admit analytic solutions in the expansion parameters. A detailed study of Borel resummation allows one to identify these solutions as Borel sums in a distinguished region in parameter space. The Stokes jumps between different Borel sums encode the BPS invariants of the underlying geometry and are captured in turn by another set of difference equations. I will further show how the Borel analysis of the NS limit connects to the exact WKB study of quantum curves. This is based on various joint works with Lotte Hollands, Arpan Saha, Iván Tulli and Jörg Teschner.