Supersymmetric reduction of 3D theories on a line segment

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 AT = 0 and AT = 1 cases flowing to the bosonic and AT = (0, 1) WZW models in 2D. Then we study the 3D AT = 2 YM-CS on the interval with the AT = (0,2) Dirichlet boundaries. It flows to a noncompact version of the AT = (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 nonperturbative effects. We also construct the 2D Landau-Ginzburg models flowing to the similar sigma models.