13 research outputs found
Ectoplasm with an Edge
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.Comment: 25 page