Gauge-invariant observables, gravitational dressings, and holography in AdS

TL;DR

This paper constructs gauge-invariant observables in AdS space using gravitational dressings, explores their algebra and boundary symmetries, and discusses implications for holography and the boundary theory correspondence.

Contribution

It introduces a perturbative method for constructing gauge-invariant observables in AdS and analyzes their algebra and boundary symmetry actions, highlighting the role of boundary conditions.

Findings

Explicit gravitational dressings lead to nonlocal observable algebra.

Boundary generators of AdS isometries are explicitly derived.

Holographic map construction requires solving non-perturbative constraints.

Abstract

This paper explores construction of gauge (diffeomorphism)-invariant observables in anti de Sitter (AdS) space and the related question of how to find a "holographic map" providing a quantum equivalence to a boundary theory. Observables are constructed perturbatively to leading order in the gravitational coupling by gravitationally dressing local field theory operators in order to solve the gravitational constraints. Many such dressings are allowed and two are explicitly examined, corresponding to a gravitational line and to a Coulomb field; these also reveal an apparent role for more general boundary conditions than considered previously. The observables obey a nonlocal algebra, and we derive explicit expressions for the boundary generators of the SO(D-1,2) AdS isometries that act on them. We examine arguments that gravity {\it explains} holography through the role of such a boundary Hamiltonian. Our leading-order gravitational construction reveals some questions regarding how these arguments work, and indeed construction of such a holographic map appears to require solution of the non-perturbative generalization of the bulk constraint equations.