We resum the recently calculated second order kernel of the BFKL equation. That kernel can be viewed as the sum of a conformally invariant part and a running coupling part. The conformally invariant part leads to a corrected BFKL intercept as found earlier. The running couplng part of the kernel leads to a non-Regge term in the energy dependence of high energy hard scattering, as well as a Q2−d...

A family (Dλ)λ∈C of differential operators on the sphere S n is constructed. The operators are conformally covariant for the action of the subgroup of conformal transformations of S which preserve the smaller sphere Sn−1 ⊂ S. The family of conformally covariant differential operators from S to Sn−1 introduced by A. Juhl is obtained by composing these operators on S and taking restrictions to Sn−1.

Here we will consider examples of conformally flat manifolds that are conformally equivalent to open subsets of the sphere S. For such manifolds we shall introduce a Cauchy kernel and Cauchy integral formula for sections taking values in a spinor bundle and annihilated by a Dirac operator, or generalized Cauchy-Riemann operator. Basic properties of this kernel are examined, in particular we exa...

The classical Sobolev and Escobar inequalities are embedded into the same oneparameter family of sharp trace-Sobolev inequalities on half-spaces. Equality cases are characterized for each inequality in this family by tweaking a well-known mass transportation argument. The case of the Dirichlet energy corresponds to a family of variational problems on conformally flat metrics, whose absolute min...

We study the theory of Weyl conformal gravity with matter degrees of freedom in a conformally invariant interaction. Specifically, we consider a triplet of scalar fields and SO(3) non-abelian gauge fields, i.e. the Georgi-Glashow model conformally coupled to Weyl gravity. We show that the equations of motion admit solutions spontaneously breaking the conformal symmetry and the gauge symmetry, p...

In this paper we describe the behavior of solutions of the KleinGordon equation, ( g + λ)u = f , on Lorentzian manifolds (X, g) which are anti-de Sitter-like (AdS-like) at infinity. Such manifolds are Lorentzian analogues of the so-called Riemannian conformally compact (or asymptotically hyperbolic) spaces, in the sense that the metric is conformal to a smooth Lorentzian metric ĝ on X, where X ...

This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This connection is a manifestation of the general principle that the far field phenomena on a conformally compact Einstein manifold are related to conformal theories on its boundary at infinity. This relations...

1. Statement of the results This paper describes the connection between scattering matrices on conformally compact asymptotically Einstein manifolds and conformally invariant objects on their boundaries at infinity. This connection is a manifestation of the general principle that the far field phenomena on a conformally compact Einstein manifold are related to conformal theories on its boundary...

Using a Hamiltonian approach to gauged WZW models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the 1/k expansion , for any bosonic, heterotic, or type-II superstring model based on a coset G/H. We prove the following relations: (i) For type-II superstrings the conformally exact metric and dilaton are identical to those of the non-supersym...