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FIELD Phys:StringTheory
DATE August 10 (Wed), 2022
TIME 16:00-17:00
PLACE 8101
SPEAKER Thorsten Schimannek
HOST Ghim, Dongwook
INSTITUTE Sorbonne University
TITLE Counting BPS states with discrete charges in M-theory

Discrete gauge symmetries can arise in M-theory on Calabi-Yau threefolds with terminal singularities. I will argue that the Gopakumar-Vafa invariants are encoded in partition functions associated to different values of a discrete flat but topologically non-trivial B-field that stabilizes the singularities. Locally, the effect of the B-field can be interpreted as replacing each node by a non-commutative conifold. This picture allows us to derive closed expressions for the constant map contributions to the topological string partition functions on non-commutative crepant resolutions. The main example in this talk will be singular torus fibered Calabi-Yau 3-folds that share the same Jacobian fibrations as smooth genus one fibered Calabi-Yaus. Somewhat miraculously, all of the relevant partition functions can then be recovered at newly discovered non-commutative large volume limits in the stringy Kähler moduli spaces of a rich network of interconnected torus fibrations. This makes it possible to extract the Gopakumar-Vafa invariants associated to discrete charged BPS states in M-theory on singular Calabi-Yau threefolds. If time permits, I will also comment on the F-theory interpretation in terms of twisted elliptic genera and use this to deduce the 6d discrete 't Hooft anomaly. The talk is mainly based on 2108.09311 by the speaker and on work in progress with Albrecht Klemm, Sheldon Katz and Eric Sharpe. The application to anomalies is work in progress with Markus Dierigl and Paul Oehlmann.

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