Quantum sheaf cohomology on Grassmannians
arXiv:1512.08586 · doi:10.1007/s00220-016-2763-z
Abstract
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.
60 pages, LaTeX; v2:identifier added to reference; v3:typos fixed
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- A proposal for nonabelian (0,2) mirrors
- B-branes and supersymmetric quivers in 2d
- A-twisted correlators and Hori dualities
- A proposal for (0,2) mirrors of toric varieties
- Classical sheaf cohomology rings on Grassmannians
- More Toda-like (0,2) mirrors
- GLSMs for exotic Grassmannians
- A proposal for nonabelian mirrors
- Quantum Sheaf Cohomology and Duality of Flag Manifolds
- (0,2) versions of exotic (2,2) GLSMs
- Quantum cohomology from mixed Higgs-Coulomb branches
- Quantum cohomology of symplectic flag manifolds
- A survey of recent developments in GLSMs