Abstract
A minimal requirement for any strongly coupled gauge field theory to have a classical dual bulk gravity description is that one should in principle be able to recover the full geometry as encoded on the asymptotics of the spacetime. Even this requirement cannot be fulfilled with arbitrary precision simply due to the fact that the boundary data is inherently noisy. We present a statistical approach to bulk reconstruction from entanglement entropy measurements, which handles the presence of noise in a natural way. Our approach therefore opens up a novel gateway for precision holography.
Highlights
The holographic modeling of field theory phenomena starts from a known supergravity action with manifest symmetries
How the boundary is encoded in the bulk geometry is one of the pressing questions of today’s holography [1]
In addition to the likelihood (13) we place weakly informative normal priors on a⃗ and R3=4GN with standard deviation 5 around their maximum likelihood estimates. This gives us a posterior distribution which we study by drawing samples using the Hamiltonian Monte Carlo (HMC) [28]
Summary
The holographic modeling of field theory phenomena starts from a known supergravity action with manifest symmetries. Postulating an emergent classical spacetime dual necessitates a lattice formulation of the gauge field theory in the strong coupling regime This means that the boundary data inherently contain error margin from statistical sampling and the reconstructed dual geometry cannot be. We note that the extrapolation of the thermodynamic properties [22] in these same field theories supports the existence of a dual gravity description This method of applying AdS=CFT in reverse, enables predicting, e.g., the two-point functions of heavy operators [23,24,25] or Wilson loops [26,27] at different energy scales given the same external control parameters. We explain how measurements of the derivatives of the entanglement entropy with respect to the system size and the associated statistical uncertainties can be transferred to geometric quantities of bulk spacetime by statistical sampling
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