Extremal Three-point Correlators in Kerr/CFT

Abstract

We compute three-point correlation functions in the near-extremal, near-horizon region of a Kerr black hole, and compare to the corresponding finite-temperature conformal field theory correlators. For simplicity, we focus on scalar fields dual to operators ${\mathcal{O}}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $Ad{S}_5\times S^5$ three-point function in the literature. For such extremal correlators we find perfect agreement with the conformal field theory side, provided that the coupling of the cubic interaction contains a vanishing prefactor $\propto h_3-h_1-h_2$. In fact, the bulk three-point function integral for such extremal correlators diverges as $1/(h_3-h_1-h_2)$. This behavior is analogous to what was found in the context of extremal AdS/CFT three-point correlators. As in AdS/CFT our correlation function can nevertheless be computed via analytic continuation from the non-extremal case.

22 pages; v2: references added, typos corrected

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• Hidden Conformal Symmetry of Extremal Black Holes
• Hidden Conformal Symmetry of Kerr-Bolt Spacetimes
• Holographic Q-picture of Kerr-Newman-AdS-dS Black Hole
• Explaining Nonlinearities in Black Hole Ringdowns from Symmetries
• Holographic description of Kerr-Bolt-AdS-dS Spacetimes
• Hidden Conformal Symmetry of Rotating Black Hole with four Charges
• Hidden Conformal Symmetry of Extremal Kerr-Bolt Spacetimes
• Black Hole Vacua and Rotation
• Conformal Invariance and Near-extreme Rotating AdS Black Holes
• General Hidden Conformal Symmetry of 4D Kerr-Newman and 5D Kerr Black Holes
• Holographic Dual of the Reissner-Nordström Black Hole
• A definition of primary operators in $J\bar{T}$-deformed CFTs
• The Kerr-Newman/CFTs Correspondence
• An Analysis of the Wave Equation for the $U(1{)}^2$ Gauged Supergravity Black Hole