BPS indices, modularity and perturbations in quantum K-theory

Abstract

Abstract We study a perturbation family of N $$ \mathcal{N} $$ = 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.

Keywords

• Chern-Simons Theories
• Supersymmetric Effective Theories
• Wilson
• ’t Hooft and Polyakov loops
• Sigma Models