Topological M-Strings and Supergroup WZW Models

TL;DR

This paper explores how boundary conditions in topologically twisted Chern-Simons matter theories with Lie 3-algebra structures lead to supergroup WZW models, proposing a connection to low-energy theories on intersecting M-branes.

Contribution

It unifies supersymmetric and gauge invariant boundary conditions as complexified gauge invariant conditions resulting in supergroup WZW models, linking M-brane intersections to these models.

Findings

Boundary conditions unify as complexified gauge invariant conditions.

Supergroup WZW models emerge as effective theories on M-brane intersections.

Proposes a new perspective on low-energy limits of M2 and M5-brane systems.

Abstract

We study the boundary conditions in the topologically twisted Chern-Simons matter theories with the Lie 3-algebraic structure. We find that the supersymmetric boundary conditions and the gauge invariant boundary conditions can be unified as the complexified gauge invariant boundary conditions which lead to the supergroup WZW models. We propose that the low-energy effective field theories on the two-dimensional intersection of multiple M2-branes on a holomorphic curve inside K3 with two non-parallel M5-branes on the K3 are supergroup WZW models from the topologically twisted BLG-model and the ABJM-model.