Quantum K-Theory of Calabi-Yau Manifolds

Abstract

The disk partition function of certain 3d N=2 supersymmetric gauge theories computes a quantum K-theoretic ring for Kahler manifolds X. We study the 3d gauge theory/quantum K-theory correspondence for global and local Calabi-Yau manifolds with several Kahler moduli. We propose a multi-cover formula that relates the 3d BPS world-volume degeneracies computed by quantum K-theory to Gopakumar-Vafa invariants.

25p, v2: references added

References in corpus (3)

• The Hirzebruch--Riemann--Roch theorem in true genus-0 quantum K-theory
• Wilson loops in supersymmetric Chern-Simons-matter theories and duality
• Twisted Indices of 3d $\mathcal{N}=4$ Gauge Theories and Enumerative Geometry of Quasi-Maps

Cited by in corpus (12)

• Quantum K theory of symplectic Grassmannians
• BPS Indices, Modularity and Perturbations in Quantum K-theory
• Quantum K theory rings of partial flag manifolds
• WDVV equations and invariant bi-Hamiltonian formalism
• Decomposition squared
• Quantum K theory of Grassmannians, Wilson line operators, and Schur bundles
• Quantum cohomology from mixed Higgs-Coulomb branches
• Congruences on K-theoretic Gromov--Witten invariants
• Schubert line defects in 3d GLSMs, part II: Partial flag manifolds and parabolic quantum polynomials
• A survey of recent developments in GLSMs
• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
• $K$-theoretic quasimap wall-crossing