Ectoplasm with an Edge

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.

25 pages

References in corpus (7)

• On duality symmetries of supergravity invariants
• Integral invariants in maximally supersymmetric Yang-Mills theories
• The supermultiplet of boundary conditions in supergravity
• Tensor calculus for supergravity on a manifold with boundary
• D=7 / D=6 Heterotic Supergravity with Gauged R-Symmetry
• Higher order terms in an improved heterotic M theory
• Supersymmetric bulk-brane coupling with odd gauge fields

Cited by in corpus (13)

• N=1 and N=2 pure supergravities on a manifold with boundary
• Supersymmetric Chern-Simons Theory in Presence of a Boundary
• The linear multiplet and ectoplasm
• On the supersymmetry invariance of flat supergravity with boundary
• Unconventional Supersymmetry at the Boundary of AdS_4 Supergravity
• On supersymmetric Chern-Simons-type theories in five dimensions
• F-Theory on Spin(7) Manifolds: Weak-Coupling Limit
• On Supersymmetry, Boundary Actions and Brane Charges
• Superforms in Simple Six-dimensional Superspace
• Superspace de Rham Complex and Relative Cohomology
• Superforms in Five-Dimensional, $N=1$ Superspace
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
• On the geometric approach to the boundary problem in supergravity