Holographic coarsegraining: correlators from the entanglement wedge and other reduced geometries
Abstract
There is some tension between two wellknown ideas in holography. On the one hand, subregion duality asserts that the reduced density matrix associated with a limited region of the boundary theory is dual to a correspondingly limited region in the bulk, known as the entanglement wedge. On the other hand, correlators that in the boundary theory can be computed solely with that density matrix are calculated in the bulk via the GKPW or BDHM prescriptions, which require input from beyond the entanglement wedge. We show that this tension is resolved by recognizing that the reduced state is only fully identified when the entanglement wedge is supplemented with a specific infrared boundary action, associated with an endoftheworld brane. This action is obtained by coarsegraining through a variant of Wilsonian integration, a procedure that we call holographic rememorization, which can also be applied to define other reduced density or transition matrices, as well as more general reduced partition functions. We find an interesting connection with AdS/BCFT, and, in this context, we are led to a simple example of an equivalence between an ensemble of theories and a single theory, as discussed in recent studies of the black hole information problem.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2022
 DOI:
 10.1007/JHEP08(2022)118
 arXiv:
 arXiv:2201.01786
 Bibcode:
 2022JHEP...08..118G
 Keywords:

 AdSCFT Correspondence;
 GaugeGravity Correspondence;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 39+15 pages, 8 figures, v2: references and 2 paragraphs added, typos corrected