\(R^2\) corrected \(\mathrm{AdS}_2\) holography. (English) Zbl 1461.83046
Summary: We approach the problem of constructing an explicit holographic dictionary for the \(\mathrm{AdS}_2/ \mathrm{CFT}_1\) correspondence in the context of higher derivative gravitational actions in \(\mathrm{AdS}_2\) space-times. These actions are obtained by an \(S^2\) reduction of four-dimensional \(\mathcal{N} = 2\) Wilsonian effective actions with Weyl squared interactions restricted to constant scalar backgrounds. BPS black hole near-horizon space-times fall into this class of backgrounds, and by identifying the boundary operators dual to the bulk fields, we explicitly show how the Wald entropy of the BPS black hole is holographically encoded in the anomalous transformation of the operator dual to a composite bulk field. Additionally, using a 2d/3d lift, we show that the CFT holographically dual to \(\mathrm{AdS}_2\) is naturally embedded in the chiral half of the \(\mathrm{CFT}_2\) dual to the \(\mathrm{AdS}_3\) space-time, and we identify the specific operator in \(\mathrm{CFT}_1\) that encodes the chiral central charge of the \(\mathrm{CFT}_2\).
MSC:
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
| 83E05 | Geometrodynamics and the holographic principle |
| 83C45 | Quantization of the gravitational field |
| 81T35 | Correspondence, duality, holography (AdS/CFT, gauge/gravity, etc.) |
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