Axi-Dilaton Gravity in D \geq 4 Dimensional Space-Times with Torsion

We study models of axi-dilaton gravity in space-time geometries with torsion. We discuss conformal re-scaling rules in both Riemannian and non-Riemannian formulations. We give static, spherically symmetric solutions and examine their singularity structure

Monopole equations on 8-manifolds with Spin(7) holonomy

We construct a consistent set of monopole equations on eight-manifolds with Spin(7) holonomy. These equations are elliptic and admit non-trivial solutions including all the 4-dimensional Seiberg-Witten solutions as a special case.Comment: 14 pages, LATEX (No figures

The Geometry of Self-dual 2-forms

We show that self-dual 2-forms in 2n dimensional spaces determine a $n^2-n+1$ dimensional manifold ${\cal S}_{2n}$ and the dimension of the maximal linear subspaces of ${\cal S}_{2n}$ is equal to the (Radon-Hurwitz) number of linearly independent vector fields on the sphere $S^{2n-1}$. We provide a direct proof that for $n$ odd ${\cal S}_{2n}$ has only one-dimensional linear submanifolds. We exhibit $2^c-1$ dimensional subspaces in dimensions which are multiples of $2^c$, for $c=1,2,3$. In particular, we demonstrate that the seven dimensional linear subspaces of ${\cal S}_{8}$ also include among many other interesting classes of self-dual 2-forms, the self-dual 2-forms of Corrigan, Devchand, Fairlie and Nuyts and a representation of ${\cal C}l_7$ given by octonionic multiplication. We discuss the relation of the linear subspaces with the representations of Clifford algebras.Comment: Latex, 15 page

Dirac equation in spacetimes with torsion and non-metricity

Dirac equation is written in a non-Riemannian spacetime with torsion and non-metricity by lifting the connection from the tangent bundle to the spinor bundle over spacetime. Foldy-Wouthuysen transformation of the Dirac equation in a Schwarzschild background spacetime is considered and it is shown that both the torsion and non-metricity couples to the momentum and spin of a massive, spinning particle. However, the effects are small to be observationally significant.Comment: 12 pages LATEX file, no figures, to appear in Int. J. Mod. Phys.

String-Inspired Chern-Simons Modified Gravity In 4-Dimensions

Chern-Simons modified gravity models in 4-dimensions are shown to be special cases of low energy effective string models to first order in the string constant.Comment: To appear in the European Physics Journal