Quantum sheaf cohomology on Grassmannians

Jirui Guo Virginia Tech Zhentao Lu University of Oxford Eric Sharpe Virginia Tech

Mathematical Physics Algebraic Geometry arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2205.22005

Communications in Mathematical Physics, 352, (1), 135-184, 2017.12
In this paper we study the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle. Quantum sheaf cohomology is a (0,2) deformation of the ordinary quantum cohomology ring, realized as the OPE ring in A/2-twisted theories. Quantum sheaf cohomology has previously been computed for abelian gauged linear sigma models (GLSMs); here, we study (0,2) deformations of nonabelian GLSMs, for which previous methods have been intractable. Combined with the classical result, the quantum ring structure is derived from the one-loop effective potential. We also utilize recent advances in supersymmetric localization to compute A/2 correlation functions and check the general result in examples. In this paper we focus on physics derivations and examples; in a companion paper, we will provide a mathematically rigorous derivation of the classical sheaf cohomology ring.
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  title={Quantum sheaf cohomology on Grassmannians},
  author={Jirui Guo, Zhentao Lu, and Eric Sharpe},
  booktitle={Communications in Mathematical Physics},
Jirui Guo, Zhentao Lu, and Eric Sharpe. Quantum sheaf cohomology on Grassmannians. 2017. Vol. 352. In Communications in Mathematical Physics. pp.135-184. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519170243767587299.
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