Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 11, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP11(2018)074
Keywords
AdS-CFT Correspondence; Models of Quantum Gravity
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Funding
- U.S. Department of Energy, Office of Science [DE-SC0011702]
- Foundational Questions Institute [FQXi-RFP-1507]
- National Science Foundation Graduate Research Fellowship Program [1650114]
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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 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.
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