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

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

2012-02-22

arxiv.org/abs/1202.4934v2

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, notation improved, refs added

Scientific paper

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.

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