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arXiv · 2212.08655

Topological Strings on Non-Commutative Resolutions

Sheldon Katz·Albrecht Klemm·Thorsten Schimannek·Eric Sharpe
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Abstract

In this paper we propose a definition of torsion refined Gopakumar-Vafa (GV) invariants for Calabi-Yau threefolds with terminal nodal singularities that do not admit K\"ahler crepant resolutions. Physically, the refinement takes into account the charge of five-dimensional BPS states under a discrete gauge symmetry in M-theory. We propose a mathematical definition of the invariants in terms of the geometry of all non-K\"ahler crepant resolutions taken together. The invariants are encoded in the A-model topological string partition functions associated to non-commutative (nc) resolutions of the Calabi-Yau. Our main example will be a singular degeneration of the generic Calabi-Yau double cover of $\mathbb{P}^3$ and leads to an enumerative interpretation of the topological string partition function of a hybrid Landau-Ginzburg model. Our results generalize a recent physical proposal made in the context of torus fibered Calabi-Yau manifolds by one of the authors and clarify the associated enumerative geometry.

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Sheldon Katz, Albrecht Klemm, Thorsten Schimannek, Eric Sharpe. 2022-12-16. Topological Strings on Non-Commutative Resolutions. https://doi.org/10.1007/s00220-023-04896-2

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