Conformally invariant variational integrals

New Dual Conformally Invariant Off-Shell Integrals

Evidence has recently emerged for a hidden symmetry of scattering amplitudes in N = 4 super Yang-Mills theory called dual conformal symmetry. At weak coupling the presence of this symmetry has been observed through five loops, while at strong coupling the symmetry has been shown to have a natural interpretation in terms of a T-dualized AdS5. In this paper we study dual conformally invariant off...

Is mass conformally invariant ?

By using the Garfinkle, Horowitz and Strominger black hole solutions as examples, we illustrate that, with respect to the reference action functional proposed by Hawking and Horowitz, the asymp-totic mass parameter is not invariant between two conformally related static spherically symmetric metrics.

Sharp Inequalities for Functional Integrals and Traces of Conformally Invariant Operators

The intertwining operators Ad = Ad(g) on the round sphere (Sn, g) are the conformal analogues of the power Laplacians 1d/2 on the flat Rn . To each metric ρg, conformally equivalent to g, we can naturally associate an operator Ad(ρg), which is compact, elliptic, pseudodifferential of order d, and which has eigenvalues λ j (ρ); the special case d = 2 gives precisely the conformal Laplacian in th...

Minimization of Conformally Invariant Energies

Conformally Invariant Non-local Operators

On a conformal manifold with boundary, we construct conformally invariant local boundary conditions B for the conformally invariant power of the Laplacian k , with the property that ( k , B) is formally self-adjoint. These boundary problems are used to construct conformally invariant nonlocal operators on the boundary Σ, generalizing the conformal Dirichlet-to-Robin operator, with principal par...