On the Unitarity of the Gravitational S-Matrix in High Dimension

TL;DR

This work argues that in space-time dimensions $d\ge 5$, the gravitational S-matrix cannot be unitary on the conventional Fock space due to infrared effects: final states are normalizable graviton coherent states with vanishing overlaps with finite-particle sectors at high energy, whether described through soft radiation or Hawking radiation from black holes. It reconciles perturbative UV unitarity with nonperturbative IR behavior by proposing an algebraic quantum scattering framework, built from a regulated AGS-like algebra on nested causal diamonds, where unitarity is defined for locally normal states rather than Fock-space amplitudes. The paper surveys supporting perspectives from BFSS matrix theory and AdS/CFT arena constructions, showing these approaches do not contradict the Fock-space nonunitarity but rather point to a broader, algebraic notion of scattering unitarity. A key open challenge is proving Poincar\'e invariance of the amplitudes within this algebraic framework and establishing a separable Hilbert-space representation for the limiting theory.

Abstract

We argue that for finite energy windows, the final states in gravitational scattering in dimension $d > 4$ are normalizable coherent states in Fock space. However, as the center of the energy window goes to infinity, black hole physics predicts that these states become orthogonal to every state with a finite number of particles. Given that the spectral measure in energy is determined by Poincare invariance, the S-matrix cannot be a unitary operator in Fock space, despite having finite matrix elements in Fock space, and satisfying perturbative unitarity, to all orders in string perturbation theory. We identify regimes in the BFSS matrix model\cite{bfss} and the definition of the S-matrix as the limit of CFT correlators\cite{polchsuss}, which point to the same conclusion. We review a scattering theory based on the quantum mechanics of a finite number of fermionic oscillators, whose algebra formally converges to the Super-Poincare covariant Awada-Gibbons-Shaw\cite{ags} algebra, and argue that a certain class of limiting states on that algebra satisfy all the properties required by physical unitarity in the algebraic formulation of quantum mechanics. The only missing ingredient for a consistent theory is a proof that the S matrix amplitudes themselves are Poincare invariant. We provide suggestive arguments, but no real proof, that this is so.

Figures (2)

• Figure 1: Symmetrically Nested Causal Diamonds
• Figure 2: 2 +1 Dimensional Section of the Holographic Depiction of Jet Scattering: Red Arcs Are Q-bits Surrounded by "Frozen Q=bits" That Decouple Them From The Bulk of the Horizon Degrees of Freedom