BPS Indices, Modularity and Perturbations in Quantum K-theory

Abstract

We study a perturbation family of N=2 3d gauge theories and its relation to quantum K-theory. A 3d version of the Intriligator-Vafa formula is given for the quantum K-theory ring of Grassmannians. The 3d BPS half-index of the gauge theory is connected to the theory of bilateral hypergeometric q-series, and to modular q-characters of a class of conformal field theories in a certain massless limit. Turning on 3d Wilson lines at torsion points leads to mock modular behavior. Perturbed correlators in the IR regime are computed by determining the UV-IR map in the presence of deformations.

arXiv comment71 pages, v2:references added

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• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• Line defect half-indices of $SU(N)$ Chern-Simons theories
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• Schubert line defects in 3d GLSMs, part I: Complete flag manifolds and quantum Grothendieck polynomials
• Elliptic Stable Envelopes for Certain Non-Symplectic Varieties and Dynamical $R$-Matrices for Superspin Chains from the Bethe/Gauge Correspondence