The first law and Wald entropy formula of heterotic stringy black holes at first order in α′

We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in α′ using Wald’s formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in α′ that can be reliably used in a comparison with the microscopic ones. Such a formula was still lacking in the literature.In the proof we use momentum maps to define covariant variations and Lie derivatives and restricted generalized zeroth laws which state the closedness of certain differential forms on the bifurcation sphere and imply the constancy of the associated potentials on it.We study the relation between our entropy formula and other formulae that have been used in the literature.

SOME NOTES ON THE MODIFIED RIEMANNIAN EXTENSION g ̃_(∇,c) ON COTANGENT BUNDLE

In this paper, we define the modified Riemannian extension g ̃_(∇,c) in the cotangent bundle T^* M, which is completely determined by its action on complete lifts of vector fields. Later, we obtain the covarient and Lie derivatives applied to the modified Riemannian extension with respect to the complete and vertical lifts of vector and kovector fields, respectively.

Infinitesimal Deformations of ECD Fields

The standard notion of Lie derivative is extended in order to include Lie derivatives of spinors, soldering forms, spinor connections and spacetime connections. These extensions are all linked together, and provide a natural framework for discussing infinitesimal deformations of Einstein-Cartan-Dirac fields in the tetrad-affine setting.

A nonabelian M5 brane Lagrangian in a supergravity background

We present a nonabelian Lagrangian that appears to have (2, 0) superconformal symmetry and that can be coupled to a supergravity background. But for our construction to work, we have to break this superconformal symmetry by imposing as a constraint on top of the Lagrangian that the fields have vanishing Lie derivatives along a Killing direction.