Interval reduction and (super)symmetry

Abstract

We study three-dimensional quantum field theories on the interval with symmetry-preserving boundary conditions. The physics and symmetries of the effective 2D theory in the IR are the main subjects of this note. We focus on the (super-)Yang-Mills-Chern-Simons (YM-CS) theories with the Dirichlet boundary conditions on both ends. We warm up with the $\mathcal{N}=0$ and $\mathcal{N}=1$ cases flowing to the bosonic and $\mathcal{N}=(0,1)$ WZW models in 2D. Then we study the 3D $\mathcal{N}=2$ YM-CS on the interval with the $\mathcal{N}=(0,2)$ Dirichlet boundaries. It flows to a non-compact version of the $\mathcal{N}=(0,2)$ WZW. We compute its perturbatively exact two-derivative effective action (i.e., the metric and the B-field), and speculate on the possibility of novel non-perturbative effects. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models.