Central Charges in Extreme Black Hole/CFT Correspondence

TL;DR

This work argues that the central charges of extremal black holes in four and five dimensions originate exclusively from the gravitational sector, even in the presence of non-gravitational fields and topological terms. Using covariant phase space and cohomological methods, the authors compute conserved charges for a general Einstein–Maxwell–scalar action with topological terms, showing that vector and scalar contributions do not alter the central charge. They derive explicit central charges in 4D and 5D and demonstrate that, with the appropriate left-moving temperature, the Cardy formula yields the Bekenstein–Hawking entropy of general extremal black holes, supporting the extreme black hole/CFT correspondence. The results hold for general near-horizon geometries in these theories and extend the Kerr/CFT framework beyond pure gravity, to other dimensions and horizon topologies (excluding T^{D-2}).

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.