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 dimensionally-reduced metrics. In this work, we generalize the approach to bulk reconstruction using light-cone cuts and propose a prescription to obtain the full higher-dimensional metric of generic spacetimes up to an overall conformal factor. We first extend the definition of light-cone 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 bulk-point singularities of correlators, and the new information in the extended cut can be extracted by using appropriate combinations of operators dual to Kaluza-Klein modes of the higher-dimensional bulk fields.

Bit threads, Einstein’s equations and bulk locality

“…While there are other methods for bulk reconstruction, e.g. [45][46][47], our comments and comparisons refer only to approaches that make explicit use of RT surfaces. Quite generally, if one hopes for a reconstruction of JHEP01(2021)193 the metric everywhere in the bulk one must start with a sufficiently dense set of extremal surfaces that probe the full manifold M .…”

Snowmass White Paper: The Analytic Conformal Bootstrap

“…Relatedly, Lorentzian signature admits a much richer array of singularities than Euclidean signature, for example the lightcone, Regge, and "bulk point" limits [21,[235][236][237]. See [238] for a recent bootstrap analysis of gauge theory correlators near a Lorentzian singularity, and [239][240][241] for a discussion of Lorentzian singularities in the context of bulk reconstruction. It was conjectured in [236] that Lorentzian singularities should be in one-to-one correspondence with position-space Landau diagrams.…”

Bulk reconstruction of metrics inside black holes by complexity

“…The Wilson loop [37] can determine both f (r) and g(r) but they are in the string frame, and they differ from the Einstein frame by a conformal factor of unknown dilaton profile. The method using the light-cone cuts [8,9,12] determines the metric up to a conformal factor. Therefore, the combination of the entanglement entropy and either the Wilson loops or the light-cone cuts can determine the metric outside the black hole horizon completely.…”

“…In this section, we provide a reconstruction formula to determine both f (r) and g(r). 12 As is described in the introduction, the reconstruction in the previous section with (2.2) is possible since the time dependence of the complexity provided just enough degree of freedom to reconstruct a single unknown metric function f (r). Therefore, for the reconstruction of both f (r) and g(r), we need another functional information in addition to the complexity.…”

“…Nevertheless, various methods have been developed to reconstruct bulk spacetime metrics by the data of dual quantum field theories (QFTs). 1 Successful methods include the holographic renormalization [5], the reconstruction using bulk geodesics and light cones [6][7][8][9][10][11][12], the reconstruction [13][14][15][16][17][18][19][20][21][22][23][24][25] using holographic entanglement entropy [26,27], 2 the inversion formula [37] of the holographic Wilson loops [38][39][40][41], and the machine learning holography [42][43][44][45][46][47]. 3 However, all of these methods do not reconstruct the static black hole 1 Here we focus on only the bulk reconstruction of spacetime metrics.…”