Membranes with a boundary
David S Berman, Daniel C Thompson
TL;DR
This work develops a framework for open, interacting membranes by introducing boundary actions in Chern-Simons–matter theories and analyzing the resulting boundary dynamics. The authors show that the gauge sector with a boundary yields a boundary non-chiral WZW string with central charge $c = \frac{k(N^2-1)}{k+N}$, consistent with the expected growth of boundary degrees of freedom, and they extend the construction to full ABJM with boundary while preserving a portion of supersymmetry. The paper then demonstrates that boundary terms generate Basu–Harvey type equations—fuzzy funnel/BPS configurations—describing membranes ending on fivebranes, and finds a boundary quartic scalar potential in the ${\cal N}=(2,0)$ ABJM setup, tying boundary dynamics to fivebrane physics. Across ${\cal N}=1$ and ${\cal N}=2$ formalisms, the analysis clarifies how to preserve half– or quarter–BPS SUSY with boundaries, and provides explicit boundary conditions and potentials that encode open-membrane boundary physics with potential fivebrane interpretations. This approach offers a structured route to probe M5-brane physics via open membranes and boundary field theories, with implications for boundary CFTs in M-theory contexts.
Abstract
We investigate the recently developed theory of multiple membranes. In particular, we consider open membranes, i.e. the theory defined on a membrane world volume with a boundary. We first restrict our attention to the gauge sector of the theory. We obtain a boundary action from the Chern-Simons terms. Secondly, we consider the addition of certain boundary terms to various Chern-Simons theories coupled to matter. These terms ensure the full bulk plus boundary action has the correct amount of supersymmetry. For the ABJM model, this construction motivates the inclusion of a boundary quartic scalar potential. The boundary dynamics obtained from our modified theory produce Basu-Harvey type equations describing membranes ending on a fivebrane. The ultimate goal of this work is to throw light on the theory of fivebranes using the theory of open membranes.