Palatini Variation in Generalized Geometry and String Effective Actions

TL;DR

This paper extends the Palatini formalism to generalized geometry, deriving a notion of Levi-Civita connection and effective string actions within Courant algebroids, enriching the geometric framework of string theory.

Contribution

It introduces a generalized Palatini variation in Courant algebroids, leading to a new concept of Levi-Civita connection and string effective actions.

Findings

Derived a generalized Levi-Civita connection from Palatini variation.

Formulated low-energy string effective actions using generalized geometry.

Connected Courant algebroid structures with string theory 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.