BPS/CFT correspondence IV: sigma models and defects in gauge theory

Abstract

Quantum field theory L 1 on spacetime X 1 can be coupled to another quantum field theory L 2 on a spacetime X 2 via the third quantum field theory L 12 living on X 12 = X 1 ∩ X 2 . We explore several such constructions with two- and four-dimensional X 1 , X 2 ’s and zero- and two-dimensional X 12 ’s, in the context of N= 2 supersymmetry, non-perturbative Dyson–Schwinger equations, and BPS/CFT correspondence. The companion paper (Nekrasov, “BPS/CFT correspondence V: BPZ and KZ equations from qq-characters”, 2017. arXiv:1711.11582 [hep-th]) will show that the BPZ and KZ equations of two-dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver N= 2 gauge theories.