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- Title
Novel Free Differential Algebras for Supergravity.
- Authors
Grassi, Pietro Antonio
- Abstract
We develop the theory of Free Integro-Differential Algebras (FIDA) extending the powerful technique of Free Differential Algebras constructed by D. Sullivan. We extend the analysis beyond the superforms to integral- and pseudo-forms used in supergeometry. It is shown that there are novel structures that might open the road to a deeper understanding of the geometry of supergravity. We apply the technique to some models as an illustration and we provide a complete analysis for D = 11 supergravity. There, it is shown how the Hodge star operator for supermanifolds can be used to analyze the set of cocycles and to build the corresponding FIDA. A new integral form emerges which plays the role of the truly dual to 4-form F (4) and we propose a new variational principle on supermanifolds.
- Subjects
SUPERGRAVITY; VARIATIONAL principles; COCYCLES; ALGEBRA; DIFFERENTIAL algebra
- Publication
Universe (2218-1997), 2023, Vol 9, Issue 8, p376
- ISSN
2218-1997
- Publication type
Article
- DOI
10.3390/universe9080376