Supergravity Actions with Integral Forms

Abstract

Integral forms provide a natural and powerful tool for the construction of supergravity actions. They are generalizations of usual differential forms and are needed for a consistent theory of integration on supermanifolds. The group geometrical approach to supergravity and its variational principle are reformulated and clarified in this language. Central in our analysis is the Poincare' dual of a bosonic manifold embedded into a supermanifold. Finally, using integral forms we provide a proof of Gates' so-called "Ectoplasmic Integration Theorem", relating superfield actions to component actions.

36 pages, LaTex, corrected some misprints to match the published version in NPB

References in corpus (9)

• Multiloop Amplitudes and Vanishing Theorems using the Pure Spinor Formalism for the Superstring
• Component Actions from Curved Superspace: Normal Coordinates and Ectoplasm
• Ectoplasm Has No Topology
• Picture changing operators in supergeometry and superstring theory
• New Geometrical Approach to Superstrings
• Super-Chern-Simons Theory as Superstring Theory
• Cech and de Rham Cohomology of Integral Forms
• Ectoplasm & Superspace Integration Measure for 2D Supergravity with Four Spinorial Supercurrents
• Integration of Superforms and Super-Thom Class

Cited by in corpus (27)

• The Geometry of Supermanifolds and New Supersymmetric Actions
• Hodge Dualities on Supermanifolds
• The Integral Form of Supergravity
• Supergravity in the group-geometric framework: a primer
• Holst-MacDowell-Mansouri action for (extended) supergravity with boundaries and super Chern-Simons theory
• $\mathcal{N}=2$ AdS${}_4$ supergravity, holography and Ward identities
• M5-brane in the superspace approach
• Chern-Simons Theory on Supermanifolds
• One-Dimensional Super Calabi-Yau Manifolds and their Mirrors
• Covariant hamiltonian for gravity coupled to $p$-forms
• Superforms in Five-Dimensional, $N=1$ Superspace
• Super Cartan geometry and the super Ashtekar connection
• Super Quantum Mechanics in the Integral Form Formalism
• Super fiber bundles, connection forms, and parallel transport
• Supersymmetric Wilson Loops via Integral Forms
• Wess-Zumino and Super Yang-Mills Theories in D=4 Integral Superspace
• Supergravities and Branes from Hilbert-Poincaré Series
• Integral representations in supermanifolds: super Hodge duals, PCOs and Liouville forms
• Surface Operators in Superspace
• The Hodge Operator Revisited
• Chern-Simons Supergravity on Supergroup Manifolds
• The Integral Form of D=3 Chern-Simons Theories Probing ${\mathbb{C}}^n/\Gamma$ Singularities
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Gauge supergravity in $D=2+2$
• On the geometric approach to the boundary problem in supergravity
• Power to Integral Forms
• $\mathrm{D}=10$ Super-Yang-Mills Theory and Poincaré Duality in Supermanifolds