The Super BMS Algebra, Scattering and Holography

TL;DR

The paper advocates a gravity-scattering framework built around the super-BMS algebra to achieve infrared-finite amplitudes, recasting the theory in a momentum-space dual to null infinity and employing jet-like states. Infrared singularities are regulated via Holographic Space-Time using finite causal diamonds, which impose a trajectory-dependent but ultimately Lorentz-invariant structure through consistency overlaps. It further extends the construction to massive particles, explores AdS limits, and discusses how holographic regulators yield a connection to AdS/CFT UV/IR behavior. The work aims to unify IR physics, holography, and gravitational scattering into a coherent, potentially discrete moduli framework with broad implications for quantum gravity.

Abstract

I propose that the proper framework for gravitational scattering theory is the rep- resentation theory of the super-BMS algebra of Awada, Gibbons and Shaw[1], and its generalizations. Certain representation spaces of these algebras generalize the Fock space of massless particles. The algebra is realized in terms of operator valued measures on the momentum space dual to null infinity, and particles correspond to smearing these measures with delta functions. I conjecture that scattering amplitudes defined in terms of characteristic measures on finite spherical caps, the analog of Sterman-Weinberg jets[2], will have no infrared (IR) divergences. An important role is played by singular functions concentrated at zero momentum, and I argue that the formalism of Holographic Space- Time is the appropriate regulator for the singularities. It involves a choice of a time-like trajectory in Minkowski space. The condition that physics be independent of this choice of trajectory is a strong constraint on the scattering matrix. Poincare invariance of S is a particular consequence of this constraint. I briefly sketch the modifications of the formalism, which are necessary for dealing with massive particles. I also sketch how it should generalize to AdS space-time, and in particular show that the fuzzy spinor cutoff of HST implements the UV/IR correspondence of AdS/CFT.