Bulk reconstruction of metrics with a compact space asymptotically
Abstract
Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is the case for any asymptotically locally AdS_{n} × S ^{k} spacetime. Almost all previous work on metric reconstruction ignores these dimensions and would thus at most apply to dimensionallyreduced metrics. In this work, we generalize the approach to bulk reconstruction using lightcone cuts and propose a prescription to obtain the full higherdimensional metric of generic spacetimes up to an overall conformal factor. We first extend the definition of lightcone cuts to include information about the asymptotic compact dimensions, and show that the full conformal metric can be recovered from these extended cuts. We then give a prescription for obtaining these extended cuts from the dual field theory. The location of the usual cuts can still be obtained from bulkpoint singularities of correlators, and the new information in the extended cut can be extracted by using appropriate combinations of operators dual to KaluzaKlein modes of the higherdimensional bulk fields.
 Publication:

Journal of High Energy Physics
 Pub Date:
 August 2020
 DOI:
 10.1007/JHEP08(2020)108
 arXiv:
 arXiv:2003.08409
 Bibcode:
 2020JHEP...08..108H
 Keywords:

 AdSCFT Correspondence;
 Gaugegravity correspondence;
 Conformal Field Theory;
 Large Extra Dimensions;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 32 pages, 6 figures