Riemannian geometry in four dimensions, including Einstein’s equations, can be described by means of a connection that annihilates a triad of two-forms (rather than a tetrad of vector fields). Our treatment of the conformal factor of the metric differs from the original presentation of this result, due to ’tHooft. In the action the conformal factor now appears as a field to be varied. Email add...

Abstract We find an explicit formula for the conformal vector of any quantum affine W -algebra in its free field realization.

The physical states in a world-volume model of a non-critical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R × S 3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally...

The physical states in a world-volume model of a non-critical 3-brane are systematically constructed using techniques of four-dimensional conformal field theories on R × S 3 developed recently. Invariant combinations of creation modes under a special conformal transformation provide building blocks of physical states. Any state can be created by acting with such building blocks on a conformally...

The aim of this paper is to describe the geometry of conformal structures in Lorentzian signature, which admit a lightlike conformal Killing vector field whose corresponding adjoint tractor acts as complex structure on the standard tractor bundle of conformal geometry. Key to the treatment of this problem is CR-geometry and the Fefferman construction. In fact, we will consider here partially in...

The main result of this paper is that a Lorentzian manifold is locally conformally equivalent to a manifold with recurrent lightlike vector field and totally isotropic Ricci tensor if and only if its conformal tractor holonomy admits a 2-dimensional totally isotropic invariant subspace. Furthermore, for semi-Riemannian manifolds of arbitrary signature we prove that the conformal holonomy algebr...