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

TL;DR

This paper investigates the coupling of quantum field theories via defects in various dimensions within the context of supersymmetry and BPS/CFT correspondence, revealing how surface defects relate to conformal field theory equations.

Contribution

It introduces new constructions of coupled quantum field theories with defects across different dimensions in supersymmetric settings, linking them to conformal field theory equations.

Findings

Surface defects in quiver $ abla=2$ gauge theories obey BPZ and KZ equations.

Exploration of coupled QFTs in diverse dimensional configurations.

Connections established between gauge theory defects and conformal field 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 $X_{12} = X_{1} \cap X_{2}$. 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 $\mathcal{N}=2$ supersymmetry, non-perturbative Dyson-Schwinger equations, and BPS/CFT correspondence. The companion paper will show that the BPZ and KZ equations of two dimensional conformal field theory are obeyed by the half-BPS surface defects in quiver $\mathcal{N}=2$ gauge theories.