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arXiv · 1004.1174

Extremal Three-point Correlators in Kerr/CFT

Melanie Becker·Sera Cremonini·Waldemar Schulgin
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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 ${\cal O}_h$ whose conformal dimensions obey $h_3=h_1+h_2$, which we name \emph{extremal} in analogy with the classic $AdS_5 \times S^5$ 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.

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Melanie Becker, Sera Cremonini, Waldemar Schulgin. 2010-07-13. Extremal Three-point Correlators in Kerr/CFT. https://doi.org/10.1007/jhep02(2011)007

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