Palatini Variation in Generalized Geometry and String Effective Actions

Abstract

We develop the Palatini formalism within the framework of generalized Riemannian geometry of Courant algebroids. In this context, the Palatini variation of a generalized Einstein-Hilbert-Palatini action - formed using a generalized metric, a Courant algebroid connection (in contrary to the ordinary case, not necessarily a torsionless one) and a volume form - leads naturally to a proper notion of a generalized Levi-Civita connection and low-energy effective actions of string theory.

References in corpus (8)

• Non-geometric strings, symplectic gravity and differential geometry of Lie algebroids
• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection
• Towards an invariant geometry of double field theory
• Poisson-Lie T-duality and Courant algebroids
• Deformed graded Poisson structures, Generalized Geometry and Supergravity
• Kaluza-Klein Reduction of Low-Energy Effective Actions: Geometrical Approach
• Effective Actions for $\sigma$-Models of Poisson-Lie Type
• Dirac geometry, quasi-Poisson actions and D/G-valued moment maps

Cited by in corpus (4)

• Supergravity without gravity and its BV formulation
• On the Equivalence of Generalized Ricci Curvatures
• Courant algebroid lifts and curved Courant algebroids
• Flat Generalized Connections on Courant Algebroids