Abstract
If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries. Holography has been believed to be a property of gravitational (or string) theories, but not of non-gravitational theories; specifically Marolf has argued that it originates from the gauge symmetries and constraints of gravity. These observations suggest study of the assumed holographic map as a function of the gravitational coupling G. The zero coupling limit gives ordinary quantum field theory, and is therefore not necessarily expected to be holographic. This, and the structure of gravity at non-zero G, raises important questions about the full map. In particular, construction of a holographic map appears to require as input a solution of the nonperturbative analog of the bulk gravitational constraints, that is, the unitary bulk evolution. Moreover, examination of the candidate boundary algebra, including the boundary hamiltonian, reveals commutators that don’t close in the usual fashion expected for a boundary theory.
Highlights
Near the boundary, it does not exhibit the closure properties that are expected for constructing a holographic map to a boundary theory
If holography is an equivalence between quantum theories, one might expect it to be described by a map that is a bijective isometry between bulk and boundary Hilbert spaces, preserving the hamiltonian and symmetries
Holography has been believed to be a property of gravitational theories, but not of non-gravitational theories; Marolf has argued that it originates from the gauge symmetries and constraints of gravity
Summary
While we don’t presently understand the complete mathematical structure on the bulk HB, we do expect that we have a good approximate description of its structure in a weak gravity limit. We expect a valid description of physics via weak gravity and local QFT to hold in scattering where CM energies of any subprocess (including multi-particle subprocesses) don’t exceed a “locality bound [14,15,16],” given in terms of the CM separation between particles ∆x. In either HLE or HLB, one expects that gravitational effects in amplitudes are accounted for via perturbative gravity, incorporating graviton exchange and radiation; in the case of HLB, exchange of multiple gravitons (loops) is relevant, but can be, e.g., treated as eikonalized single graviton exchange, so that strong gravity effects are not relevant This can be explained in terms of the small momentum transfer carried by any single graviton line (due to “momentum fractionation”); for further discussion, see, e.g., [18]. Such states and their evolution can be thought of as being accurately described entirely within QFT
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