Thermal/Black hole phase transition and entanglement entropy in (2 + 1)D

We consider a one parameter family of holographic solutions in classical string theory in three spacetime dimensions. In Euclidean space, the solutions interpolate smoothly without developing a conical singularity between the cigar black hole times a (non contractible) spatial circle and a thermal solution which has a (non contractible) temporal circle. We study the phase transition and the holographic entanglement entropy.