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

Authors :: Nikita Nekrasov
Publication Year :: 2017
Publisher :: arXiv, 2017.
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.<br />Comment: 43 pages, paper 4 of 5; v2. refs added, discussion of line operators added; v3. refs added, typos fixed, some clarifications, version to appear in the LMP