Central Charges in Extreme Black Hole/CFT Correspondence

TL;DR

This paper confirms that non-gravitational fields do not contribute to the central charges in the Kerr/CFT correspondence for extremal black holes by deriving conserved charges in Einstein-Maxwell-scalar theories and reproducing entropy.

Contribution

It provides a detailed derivation of conserved charges including non-gravitational fields and confirms their negligible effect on central charges in extremal black hole/CFT correspondence.

Findings

Central charges from non-gravitational fields vanish.

The Bekenstein-Hawking entropy is reproduced using the Cardy formula.

The results hold in four and five-dimensional theories.

Abstract

The Kerr/CFT correspondence has been recently broadened to the general extremal black holes under the assumption that the central charges from the non-gravitational fields vanish. To confirm this proposal, we derive the expression of the conserved charges in the Einstein-Maxwell-scalar theory with topological terms in four and five dimensions and check that the above assumption was correct. Combining the computed central charge with the expected form of the temperature, the Bekenstein-Hawking entropy of the general extremal black holes in four and five dimensions can be reproduced by using the Cardy formula.