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Ectoplasm with an edge

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Abstract

The construction of supersymmetric invariant actions on a spacetime manifold with a boundary is carried out using the “ectoplasm” formalism for the construction of closed forms in superspace. Non-trivial actions are obtained from the pull-backs to the bosonic bodies of closed but non-exact forms in superspace; finding supersymmetric invariants thus becomes a cohomology problem. For a spacetime with a boundary, the appropriate mathematical language changes to relative cohomology, which we use to give a general formulation of off-shell supersymmetric invariants in the presence of boundaries. We also relate this construction to the superembedding formalism for the construction of brane actions, and we give examples with bulk spacetimes of dimension 3, 4 and 5. The closed superform in the 5D example needs to be constructed as a Chern-Simons type of invariant, obtained from a closed 6-form displaying Weil triviality.

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Authors and Affiliations

  1. Department of Mathematics, King’s College, University of London, Strand, London, WC2R 2LS, U.K.

    P. S. Howe

  2. Theoretical Physics Group, Imperial College London, Prince Consort Road, London, SW7 2AZ, U.K.

    T. G. Pugh, K. S. Stelle & C. Strickland-Constable

  3. Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106, U.S.A.

    K. S. Stelle

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  1. P. S. Howe
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  2. T. G. Pugh
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  3. K. S. Stelle
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  4. C. Strickland-Constable
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Correspondence to T. G. Pugh.

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ArXiv ePrint: 1104.4387v1

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Howe, P.S., Pugh, T.G., Stelle, K.S. et al. Ectoplasm with an edge. J. High Energ. Phys. 2011, 81 (2011). https://doi.org/10.1007/JHEP08(2011)081

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  • DOI: https://doi.org/10.1007/JHEP08(2011)081

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