CFT duals of Kerr-Taub-NUT and beyond

TL;DR

This paper explores the duality between four-dimensional Kerr-Taub-NUT black holes and two-dimensional conformal field theories, deriving semiclassical formulas that match black hole entropy and discussing broader generalizations.

Contribution

It generalizes the Kerr/CFT correspondence to Kerr-Taub-NUT black holes, deriving explicit CFT dual parameters and confirming the entropy match via the Cardy formula.

Findings

Derived semiclassical temperature and central charges for the dual CFT.

Confirmed the CFT reproduces the Bekenstein-Hawking entropy.

Extended the duality to a broader class of four-dimensional black holes.

Abstract

The duality relating the four-dimensional Kerr-Taub-NUT black hole to a thermal two-dimensional CFT with central charges $c_L=c_R=12 J_0$ is analyzed in detail, generalizing an argument given recently for Kerr within the soft-hair approach. The hidden conformal symmetry is realized in the form of $Vir_L \times Vir_R$ diffeomorphisms which act non-trivially on the black hole horizon. Semiclassical formulae are derived for the temperature and central charges of the dual CFT. Assuming the applicability of the Cardy formula, these CFT quantities precisely reproduce the macroscopic Bekenstein-Hawking area law. Various further generalizations including the complete family of black holes in four dimensions are discussed.