2018/04/01 by Leonardo Castellani · 1 citation
Physics and Astronomy · Mathematics · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Homotopy and Cohomology in Algebraic Topology
paper · doi:10.1002/prop.201800014
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 off‐shell supergravities and Chern‐Simons supergravity are discussed in detail. A cursory account of 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 dimensions are summarized in Appendices.