Heating up holography for single-trace J(T)over-bar deformations

We study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [1]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS(3) background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS3 factor. The dual field theory is conjectured to be a single-trace version of a JT over bar (T) over bar -deformed CFT at finite temperature. As evidence for the correspondence we show that the spectrum of strings winding on the deformed background agrees with the spectrum of JT over bar (T) over bar -deformed CFTs. Furthermore, we show that the gravitational charges of the black string match the averaged charges of a thermal ensemble in the dual field theory. Finally, we reproduce the Bekenstein-Hawking entropy of the black string from the microscopic density of states of JT over bar (T) over bar -deformed CFTs.