Extremal Three-point Correlators in Kerr/CFT

TL;DR

This paper calculates extremal three-point correlators in Kerr/CFT, demonstrating their agreement with conformal field theory predictions and revealing divergence behavior similar to AdS/CFT cases.

Contribution

It provides the first detailed computation of extremal three-point functions in Kerr/CFT and shows their divergence structure and analytic continuation from non-extremal cases.

Findings

Perfect agreement with CFT correlators for extremal cases

Divergence of bulk three-point function as 1/(h3 - h1 - h2)

Analytic continuation from non-extremal correlators

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.