Multiple Self-Dual Strings on M5-Branes

TL;DR

The paper introduces a boundary-degrees-of-freedom method to restore gauge invariance and conformal symmetry for twisted Chern-Simons matter theories, notably the ABJM model with boundary. By embedding boundary Wess-Zumino-Witten sectors and appropriate boundary kinetic terms, the authors derive a gauge- and conformally invariant action for open M2-branes ending on M5-branes and, in the supersymmetric extension, construct a ${ m N}=(4,4)$ boundary ABJM theory on a $U(2N) imes U(2N)$ group manifold. This framework yields a concrete action for multiple self-dual strings, including boundary WZW dynamics and a quartic boundary potential constrained by supersymmetry, and reveals a $U(2N) imes U(2N)$ Kac-Moody current algebra on the string worldsheet. The results offer a self-consistent description of M2–M5 intersections with boundary degrees of freedom, with implications for non-abelian tensor dynamics, brane intersections, and potential links to Horava–Witten and heterotic setups.

Abstract

We show how to define Chern-Simons matter theories with boundary. Rather than imposing boundary conditions, we introduce new boundary degrees of freedom from the beginning and show how they can be used to cancel the gauge non-invariance of the Chern-Simons action. We apply this method to the ABJM theory with boundary. By imposing also boundary conformal invariance, we determine the required boundary action. This result allows us to derive the action for the multiple self-dual strings living on M5-branes.