Quantum gravitational information and flat holography

Abstract

A semiclassical analysis shows that black holes evaporate by emitting thermal Hawking radiation, leading to a violation of unitarity. Holography, which itself was inspired by the area scaling of black hole entropy, recently motivated quantum corrections to the black hole entropy through the Quantum Extremal Surface (QES) prescription, leading to the island proposal. Islands provide the necessary additional degrees of freedom that purify the outgoing radiation and preserve unitarity during evaporation. Islands were originally analytically studied in two-dimensional gravity. In higher dimensions, progress is limited due to the lack of explicit results for entanglement entropy (EE) of QFT states in a subregion on a higher-dimensional black hole background, which is an input to the QES prescription. We analyse entanglement entropy in particular curved backgrounds using the holographic Ryu-Takayanagi prescription. We then develop a more general systematic analysis of the properties of entanglement entropy in curved backgrounds using the replica approach. We explore the analytic (q - 1) expansion of Rényi q-entropy and its variations; our setup applies to generic variations, from symmetry transformations to variations of the background metric or entangling region. Our methodology elegantly reproduces and generalises results from the literature on entanglement entropy in different dimensions, backgrounds, and states. We use our analytic expansions to explore the behaviour of entanglement entropy in static black hole backgrounds under specific scaling transformations. Using these results, we find particular conditions on the outgoing black hole radiation spectrum for the presence of islands that restore unitarity in black hole evaporation.

We then discuss holography in asymptotically flat spacetimes using the Carrollian approach and the flat limit of AdS/CFT. Theories on degenerate null backgrounds are Carrollian (speed of light c to 0 limit of QFTs), hence these capture massless scattering between null infinities. Carrollian conformal field theories (CCFTs) are being explored as putative duals to massless scattering in asymptotically flat spacetimes. We consider the momentum space Ward identities of Carrollian conformal field theories involving scalar operators and explicitly solve to obtain the 2 and 3-point correlators. We also analyze the Carrollian limit (vanishing speed of light c to 0) of CFT 2 and 3-point functions of scalar operators in momentum space and obtain these correlators. We further discuss a generating functional for these Carrollian CFT correlators analogous to AdS/CFT. Starting with scalar fields in flat space written in coordinates adapted to null infinities, we compute the classical on-shell action. With suitable boundary conditions and source at null infinities, we show that this generates the CCFT correlators derived earlier.

A complementary approach to flat holography is to take a flat limit of AdS/CFT correlators to reproduce flat amplitudes. We also intend to systematically study massive higher-spin fields required in a consistent gravitational theory. To this end, we analyze a bulk effective field theory in AdS containing a U(1)-charged massive spin-2 field coupled to a gauge field. After holographic renormalization, we compute the one, two, and three-point functions involving two massive spin-2 fields and one gauge field. Matching with the CFT 3-point correlator of two non-conserved spin-2 operators and a conserved current, we obtain explicit mappings between the bulk minimal and gyromagnetic couplings and the boundary OPE data. Finally, we take the flat-space limit of the momentum space CFT correlator and verify that the resulting amplitude matches the expected flat-space structure.

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Identifiers

ORCID for Arvind Shekar: orcid.org/0000-0001-8979-5791

ORCID for Marika Taylor: orcid.org/0000-0001-9956-601X

ORCID for Kostas Skenderis: orcid.org/0000-0003-4509-5472

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