Quantum sheaf cohomology and duality of flag manifolds

Jirui Guo Fudan University

Mathematical Physics Algebraic Geometry arXiv subject: High Energy Physics - Theory (hep-th) mathscidoc:2205.22001

Communications in Mathematical Physics, 374, (2), 661-688, 2020.5
We study the quantum sheaf cohomology of flag manifolds with deformations of the tangent bundle and use the ring structure to derive how the deformation transforms under the biholomorphic duality of flag manifolds. Realized as the OPE ring of A/2-twisted twodimensional theories with (0,2) supersymmetry, quantum sheaf cohomology generalizes the notion of quantum cohomology. Complete descriptions of quantum sheaf cohomology have been obtained for abelian gauged linear sigma models (GLSMs) and for nonabelian GLSMs describing Grassmannians. In this paper we continue to explore the quantum sheaf cohomology of nonabelian theories. We first propose a method to compute the generating relations for (0,2) GLSMs with (2,2) locus. We apply this method to derive the quantum sheaf cohomology of products of Grassmannians and flag manifolds. The dual deformation associated with the biholomorphic duality gives rise to an explicit IR duality of two A/2-twisted (0,2) gauge theories.
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  title={Quantum sheaf cohomology and duality of flag manifolds},
  author={Jirui Guo},
  booktitle={Communications in Mathematical Physics},
Jirui Guo. Quantum sheaf cohomology and duality of flag manifolds. 2020. Vol. 374. In Communications in Mathematical Physics. pp.661-688. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220519130316175758274.
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