Ectoplasm with an Edge

Details Ectoplasm with an Edge Ectoplasm with an Edge

2011-04-22

arxiv.org/abs/1104.4387v1

JHEP 1108:081,2011

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1007/JHEP08(2011)081

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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