All four-dimensional static, spherically symmetric, two-charge Abelian Kaluza-Klein black holes and their CFT duals

We derive the dual conformal field theory Virasoro algebras from the algebra of conserved diffeomorphism charges for a large class of Abelian Kaluza-Klein black holes. Under certain conditions, such as non-vanishing electric and magnetic monopole charges, the Kaluza-Klein black holes have a Reissner-Nordstrom spacetime structure. For the non-extremal charged Kaluza-Klein black holes, we use the uplifted 6D pure gravity solutions to construct a set of Killing horizon preserving diffeomorphisms. For the (non-supersymmetric) extremal black holes, we take the near-extremal near-horizon (NENH) limit and construct a one-parameter family of diffeomorphisms which preserve the Hamiltonian constraints at spatial infinity. In each case we evaluate the algebra of conserved diffeomorphism charges following Barnich, Brandt and Compere, who used a cohomological approach, and Silva, who employed a covariant-Lagrangian formalism. At the Killing horizon, it is only Silva's algebra which acquires a central charge extension and which enables us to recover the Bekenstein-Hawking black hole entropy from the Cardy formula. For the NENH geometry, the extremal black hole entropy is obtained only when the free parameter of the diffeomorphism-generating vector fields is chosen such that the central terms of the two algebras are in agreement.