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.

64 pages, LaTeX

References in corpus (7)

• Defects and Quantum Seiberg-Witten Geometry
• The Revival of (0,2) Linear Sigma Models
• Quantum K theory of symplectic Grassmannians
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• 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

Cited by in corpus (1)

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