Phase structure of higher spin geometry

We revisit the study of the phase structure of higher spin black holes carried out in arXiv:1210.0284 using the "canonical formalism". In particular we study the low as well as high temperature regimes. We show that the Hawking-Page transition takes place in the low temperature regime. The thermodynamically favoured phase changes from conical surplus to black holes and then again to conical surplus as we increase temperature. We then show that in the high temperature regime the diagonal embedding gives the appropriate description. We also give a map between the parameters of the theory near the IR and UV fixed points. This makes the "good" solutions near one end map to the "bad" solutions near the other end and vice versa.