Boundary Conditions for Interacting Membranes

TL;DR

The authors classify and construct supersymmetric boundary conditions for open membranes in both Bagger-Lambert and ABJM theories, identifying boundary configurations corresponding to M2 ending on M5, M9, and M-Wave objects. They derive Basu-Harvey-type boundary equations and SUSY projections in the BL setup, and extend the analysis to ABJM where half-BPS boundaries yield N=(4,4) supersymmetry on the boundary, especially for k=1,2 with monopole operators enabling SUSY enhancement. They address gauge anomalies at the boundary for Chern-Simons terms, proposing boundary gauge conditions that preserve parity and gauge invariance, and discuss how half-, no-, and all-Dirichlet boundary conditions map to various open-membrane configurations, including M2–M5–M5, M2–M9, and M2–MW. The work also explores C-field backgrounds, anomaly inflows, and the spacetime interpretation of boundary SUSY via orbifold perspectives, linking worldvolume boundary dynamics to the spacetime brane picture. Overall, the paper provides a systematic framework to understand open membrane boundary physics and its implications for interacting membrane theories.

Abstract

We investigate supersymmetric boundary conditions in both the Bagger-Lambert and the ABJM theories of interacting membranes. We find boundary conditions associated to the fivebrane, the ninebrane and the M-theory wave. For the ABJM theory we are able to understand the enhancement of supersymmetry to produce the (4,4) supersymmetry of the self-dual string. We also include supersymmetric boundary conditions on the gauge fields that cancel the classical gauge anomaly of the Chern-Simons terms.