Supergravity in the group-geometric framework: a primer

Abstract

We review the group-geometric approach to supergravity theories, in the perspective of recent developments and applications. Usual diffeomorphisms, gauge symmetries and supersymmetries are unified as superdiffeomorphisms in a supergroup manifold. Integration on supermanifolds is briefly revisited, and used as a tool to provide a bridge between component and superspace actions. As an illustration of the constructive techniques, the cases of $d=3,4$ off-shell supergravities and $d=5$ Chern-Simons supergravity are discussed in detail. A cursory account of $d=10+2$ supergravity is also included. We recall a covariant canonical formalism, well adapted to theories described by Lagrangians $d$-forms, that allows to define a form hamiltonian and to recast constrained hamiltonian systems in a covariant form language. Finally, group geometry and properties of spinors and gamma matrices in $d=s+t$ dimensions are summarized in Appendices.

LaTeX, 65 pages, 2 Tables, 1 figure. v2: included Figure missing in v1, ref.s added. v3: added missing term in eq. (9.3). v4: eq. (9.41) corrected. Matches published version. v5: added missing terms in eq.s (7.21), (7.24), (7.27), (9.38), added a paragraph in Sect. 11, added ref

References in corpus (5)

• Supergravity Actions with Integral Forms
• Hidden Role of Maxwell Superalgebras in the Free Differential Algebras of D=4 and D=11 Supergravity
• The Integral Form of Supergravity
• Covariant hamiltonian for gravity coupled to $p$-forms
• Gauge supergravity in $D=2+2$

Cited by in corpus (10)

• Unconventional SUSY and Conventional Physics: A Pedagogical Review
• Generalized AdS-Lorentz deformed supergravity on a manifold with boundary
• Covariant hamiltonian for gravity coupled to $p$-forms
• On the Meaning of Local Symmetries: Epistemic-Ontological Dialectics
• Flux Quantization on 11-dimensional Superspace
• Super fiber bundles, connection forms, and parallel transport
• Covariant hamiltonian for supergravity in $d=3$ and $d=4$
• Unfolding $E_{11}$
• Hamiltonian Theory: generalizations to higher dimensions, supersymmetry and modified gravity
• On AdS${}_4$ superspace and supergravity