Ralph Blumenhagen, Andreas Deser, Erik Plauschinn, Felix Rennecke
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.
View original:
http://arxiv.org/abs/1202.4934
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