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We study three-dimensional quantum field theories on the interval withsymmetry-preserving boundary conditions. The physics and symmetries of theeffective 2D theory in the IR are the main subjects of this note. We focus onthe (super-)Yang-Mills-Chern-Simons (YM-CS) theories with the Dirichletboundary 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 modelsin 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 ofthe $\mathcal{N}=(0,2)$ WZW. We compute its perturbatively exact two-derivativeeffective action (i.e., the metric and the B-field), and speculate on thepossibility of novel non-perturbative effects. We also construct the 2DLandau-Ginzburg models flowing to the similar sigma models.

Interval reduction and (super)symmetry