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Article Dans Une Revue Commun.Math.Phys. Année : 2024

Topological Strings on Non-Commutative Resolutions

Sheldon Katz
  • Fonction : Auteur
Albrecht Klemm
  • Fonction : Auteur
Eric Sharpe
  • Fonction : Auteur

Résumé

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 Kähler 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-Kähler 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.

Dates et versions

hal-03924211 , version 1 (05-01-2023)

Identifiants

Citer

Sheldon Katz, Albrecht Klemm, Thorsten Schimannek, Eric Sharpe. Topological Strings on Non-Commutative Resolutions. Commun.Math.Phys., 2024, 405 (3), pp.62. ⟨10.1007/s00220-023-04896-2⟩. ⟨hal-03924211⟩
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