Palatini-Lovelock-Cartan Gravity - Bianchi Identities for Stringy Fluxes

TL;DR

This paper develops a Palatini formulation of gravity with torsion and fluxes, proposing new Bianchi identities for stringy fluxes and exploring their relation to string theory corrections.

Contribution

It introduces a Palatini-Lovelock-Cartan gravity framework with fluxes, deriving Bianchi identities for non-geometric fluxes using the Schouten-Nijenhuis bracket.

Findings

Derived Bianchi identities for Q- and R-fluxes including derivatives and curvature terms.

Proposed a conjecture for general Palatini-Lovelock-Cartan gravity.

Explored connections between torsional gravity and string-effective actions.

Abstract

A Palatini-type action for Einstein and Gauss-Bonnet gravity with non-trivial torsion is proposed. Three-form flux is incorporated via a deformation of the Riemann tensor, and consistency of the Palatini variational principle requires the flux to be covariantly constant and to satisfy a Jacobi identity. Studying gravity actions of third order in the curvature leads to a conjecture about general Palatini-Lovelock-Cartan gravity. We point out potential relations to string-theoretic Bianchi identities and, using the Schouten-Nijenhuis bracket, derive a set of Bianchi identities for the non-geometric Q- and R-fluxes which include derivative and curvature terms. Finally, the problem of relating torsional gravity to higher-order corrections of the bosonic string-effective action is revisited.