Novel Free Differential Algebras for Supergravity
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/9/8/376 |
| Summary: | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>F</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow></msup></semantics></math></inline-formula> and we propose a new variational principle on supermanifolds. |
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| ISSN: | 2218-1997 |