Dual CFT on Nariai limit for Kerr-Sen-dS black holes

Abstract

In this work, we study the Kerr-Sen-de Sitter black hole~(BH) in the Nariai limit where the event and cosmological horizon coincide. We show that the near-horizon Kerr-Sen-de Sitter black hole in Nariai limit is a fiber over AdS$_2$ with an appropriate coordinate transformation, instead of fiber over dS$_2$. Hence, we can compute the associated central charge and CFT temperature by using the Kerr/CFT method. It is remarkably exhibited that through Cardy's growth of states, the Bekenstein-Hawking entropy on cosmological horizon is reproduced. Moreover, we show that the radial equation of the quantum scalar field in $J$- and $Q$-pictures on this charged rotating background in Nariai limit can be portrayed in quadratic Casimir operator form with $SL(2,R)\times SL(2,R)$ isometry. We also compute the corresponding thermodynamic quantities from CFT to find the absorption cross-section and real-time correlator in $J$-picture. In $Q$-picture, we do not find a well-defined CFT description. We then extend the study of quantum scalar field in Nariai limit for Kerr-Newman-dS black hole solution and show that the hidden conformal symmetry on this black hole's background in in $J$- and $Q$-pictures is well-defined.