Abstract
Variants of the black hole information paradox are studied in Type IIB string theory setups that realize four-dimensional gravity coupled to a bath. The setups are string theory versions of doubly-holographic Karch/Randall brane worlds, with black holes coupled to non-gravitating and gravitating baths. The 10d versions are based on fully backreacted solutions for configurations of D3, D5 and NS5 branes, and admit dual descriptions as mathcal{N} = 4 SYM on a half space and 3d {T}_{rho}^{sigma } [SU(N)] SCFTs. Island contributions to the entanglement entropy of black hole radiation systems are identified through Ryu/Takayanagi surfaces and lead to Page curves. Analogs of the critical angles found in the Karch/Randall models are identified in 10d, as critical parameters in the brane configurations and dual field theories.
Highlights
Theories of gravity in which the graviton mass can be controlled, including theories with massless gravitons
Starting point are the discussions of islands and Page curves in general 5d Karch/Randall models [12,13,14,15,16], which can be used to model gravitating systems coupled to non-gravitating and gravitating baths
Islands and Page curves in Karch/Randall models: the Karch/Randall models for 4d gravity coupled to a non-gravitating bath are based on a part of AdS5 cut off by an end-of-the-world (ETW) brane extending along an AdS4 slice (figure 1(a))
Summary
The general local form of the AdS4 × S2 × S2 × Σ solutions that will be used here was constructed in [23, 24]. Comparing to the 5d Karch/Randall models, the closing off of the asymptotic AdS5 × S5 region corresponds to the introduction of the second ETW brane in figure 1(b). Solutions with more general arrangements of 5-brane sources (poles in ∂h1/2) and no asymptotic AdS5 × S5 region describe configurations of D3-branes suspended between D5 and NS5 branes that can be characterized by two Young tableaux ρ and σ, which determine how precisely the D3-branes terminate on the 5-branes. For solutions with AdS5 × S5 region and semi-infinite D3-branes the dual field theory is N = 4 SYM on a half space coupled to a 3d Tρσ[SU(N )] SCFT on the boundary [25]. The free energies obtained holographically were matched to field theory computations using supersymmetric localization for the former in [35, 36] and for the latter in [37]
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