Note on Kerr/CFT correspondence in a first order formalism

TL;DR

This paper investigates the Kerr/CFT correspondence within a first order gravity formalism, demonstrating that the Holst term does not affect the charge algebra and reproducing known results for the Palatini action.

Contribution

It extends the Kerr/CFT analysis to first order gravity formulations, clarifying the role of the Holst term and reproducing second order results.

Findings

Holst term does not contribute to the charge algebra

Reproduces second order formulation results in first order formalism

Confirms the Kerr/CFT correspondence in a new formalism

Abstract

In symmetry based approaches to black hole entropy, we calculate the central charge of the Virasoro algebra in the first order formulation of gravity for both Palatini and Holst actions. In these calculations, we made use of the NHEK metric and the Kerr-CFT correspondence. For the Palatini action the results obtained in the second order formulation are reproduced. We also argue that the Holst term does not contribute to the charge algebra no matter what geometry/boundary conditions one is considering.