Current Algebra on the Conformal Boundary and the Variables of Quantum Gravity

Abstract

I argue that scattering theory for massless particles in Minkowski space should be reformulated as a mapping between past and future representations of an algebra of densities on the conformal boundary. These densities are best thought of as living on the momentum space light cone dual to null infinity, which describes the simultaneous eigenstates of the BMS generators. The currents describe the flow of other quantum numbers through the holographic screen at infinity. They are operator valued measures on the momentum light cone, with non-zero support at $P = 0$, which is necessary to describe finite flows of total momentum, with zero energy-momentum density, on the asymptotic holographic screen. Jet states, the closest approximation to the conventional notion of asymptotic particle state, have finite momentum flowing out through spherical caps of finite opening angle, with the zero momentum currents vanishing in annuli surrounding these caps. Although these notions are valid both in field theory and quantum gravity, I'll argue that they form the basis for understanding the holographic/covariant entropy principle in the latter framework, where the densities form a complete set of operators. The variables on a finite area holographic screen are restrictions of those at infinity. The restriction is implemented by a cutoff on the Euclidean Dirac spectrum on the screen, which is a generalized UV/IR correspondence.