A Lagrangian for self-dual strings

Abstract

We propose a Lagrangian for the low-energy theory that resides at the (1 + 1)-dimensional intersection of N semi-infinite M2-branes ending orthogonally on M M5-branes in ${\mathbb{R}}^{1,2}\times {\mathbb{C}}^4/{\mathbb{Z}}_k$ (for arbitrary positive integers N, M, k). We formulate this theory as a 2d boundary theory with explicit $\mathcal{N}=\left(1,\;1\right)$ supersymmetry that contains two superfields in the bi-fundamental representation of U(N )×U(M ) interacting with the (2+1)-dimensional U(N ) _k × U(N )_−k ABJM Chern-Simons-matter theory in the bulk. We postulate that the boundary theory exhibits in the deep infrared supersymmetry enhancement to $\mathcal{N}=\left(4,\;2\right)$, or $\mathcal{N}=\left(4,\;4\right)$ depending on the value of k. Arguments in favor of the proposal follow from the study of the open string theory of a U-dual type IIB Hanany-Witten setup. To formulate the bulk-boundary interactions special care is taken to incorporate all the expected boundary effects on gauge symmetry, supersymmetry, and other global symmetries.