A-branes, foliations and localization

Sibasish Banerjee Weyertal 86-90, Department of Mathematics, University of Cologne, 50679, Cologne, Germany; Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany Pietro Longhi Institute for Theoretical Physics, ETH Zurich, 8093, Zurich, Switzerland Mauricio Andrés Romo Jorquera Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Symplectic Geometry Algebraic Geometry arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2207.34001

arXiv, 2022.1
This paper studies a notion of enumerative invariants for stable A-branes, and discusses its relation to invariants defined by spectral and exponential networks. A natural definition of stable A-branes and their counts is provided by the string theoretic origin of the topological A-model. This is the Witten index of the supersymmetric quantum mechanics of a single D3 brane supported on a special Lagrangian in a Calabi-Yau threefold. Geometrically, this is closely related to the Euler characteristic of the A-brane moduli space. Using the natural torus action on this moduli space, we reduce the computation of its Euler characteristic to a count of fixed points via equivariant localization. Studying the A-branes that correspond to fixed points, we make contact with definitions of spectral and exponential networks. We find agreement between the counts defined via the Witten index, and the BPS invariants defined by networks. By extension, our definition also matches with Donaldson-Thomas invariants of B-branes related by homological mirror symmetry.
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  title={A-branes, foliations and localization},
  author={Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera},
Sibasish Banerjee, Pietro Longhi, and Mauricio Andrés Romo Jorquera. A-branes, foliations and localization. 2022. In arXiv. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220706143822751969545.
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