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A \(\mathrm{dS}_{3}\) holography at dimension two. (English) Zbl 1418.83052

Summary: Holography can provide a microscopic interpretation of a gravitational solution as corresponding to a particular CFT state: the asymptotic expansion in gravity encodes the expectation values of operators in the dual CFT state. Such a correspondence is particularly valuable in black hole physics. We study supersymmetric D1-D5-P black holes, for which recently constructed microstate solutions known as “superstrata” provide strong motivation to derive the explicit D1-D5 holographic dictionary for CFT operators of total dimension two. In this work we derive the explicit map between one-point functions of scalar chiral primaries of dimension (1, 1) and the asymptotic expansions of families of asymptotically \(\mathrm{AdS}_{3} \times S^3 \times \mathcal{M}\) supergravity solutions, with \(\mathcal{M}\) either T4 or K3. We include all possible mixings between single-trace and multi-trace operators. We perform several tests of the holographic map, including new precision holographic tests of superstrata, that provide strong supporting evidence for the proposed dual CFT states.

MSC:

83E05 Geometrodynamics and the holographic principle
83E30 String and superstring theories in gravitational theory
83C57 Black holes
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
14J28 \(K3\) surfaces and Enriques surfaces

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