Quantum cohomology from mixed Higgs-Coulomb branches

Abstract

We generalize Coulomb-branch-based gauged linear sigma model (GLSM)-based computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the IR phase of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. Here, we systematically extend to cases for which the IR phase is a mixture of Coulomb and Higgs branches, where the latter is a Landau-Ginzburg orbifold. We describe the state spaces and products of corresponding operators in detail, comparing a geometric phase description, where the OPE ring is quantum cohomology, to the IR description in terms of Coulomb and Higgs branch states. As a concrete test of our methods, we compare to existing mathematics results for quantum cohomology rings of hypersurfaces in projective spaces in numerous examples.

arXiv comment64 pages, LaTeX

References in corpus (28)

• Phases of $N=2$ Theories In Two Dimensions
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Cluster decomposition, T-duality, and gerby CFT's
• Defects and Quantum Seiberg-Witten Geometry
• Non-birational twisted derived equivalences in abelian GLSMs
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Computing the Complete Massless Spectrum of a Landau-Ginzburg Orbifold
• Summing the Instantons in Half-Twisted Linear Sigma Models
• Notes on Certain (0,2) Correlation Functions
• The Revival of (0,2) Linear Sigma Models
• Half-Twisted Correlators from the Coulomb Branch
• On the Fukaya category of a Fano hypersurface in projective space
• Physical aspects of quantum sheaf cohomology for deformations of tangent bundles of toric varieties
• On the Structure of the Small Quantum Cohomology Rings of Projective Hypersurfaces
• Quantum K theory of symplectic Grassmannians
• The Coulomb Branch in Gauged Linear Sigma Models
• Hybrid conformal field theories
• A-Model Correlators from the Coulomb Branch
• Quantum sheaf cohomology on Grassmannians
• A Mathematical Theory of Quantum Sheaf Cohomology
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• Wilson loop algebras and quantum K-theory for Grassmannians
• Quantum K-Theory of Calabi-Yau Manifolds
• Classical sheaf cohomology rings on Grassmannians
• On Phases of 3d $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Hybrid models for homological projective duals and noncommutative resolutions
• On genus-0 invariants of Calabi-Yau hybrid models
• Quantum Sheaf Cohomology and Duality of Flag Manifolds

Cited by in corpus (1)

• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials