The coupling between Chern-Simons Theories and matter sources defined by branes of different dimensionalities is examined. It is shown that the standard coupling to membranes, such as the one found in supergravity or in string theory, does not operate in the same way for CS theories; the only p-branes that naturally couple seem to be those with p = 2n; these p-branes break the gauge symmetry (and supersymmetry) in a controlled and sensible manner.
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Edelstein, J.D., Zanelli, J. (2009). Sources for Chern-Simons theories. In: Zanelli , J., Henneaux, M. (eds) Quantum Mechanics of Fundamental Systems: The Quest for Beauty and Simplicity. Springer, New York, NY. https://doi.org/10.1007/978-0-387-87499-9_8
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