One loop partition function for topologically massive higher spin gravity

We calculate the one loop partition function for topologically massive higher spin gravity (TMHSG) for arbitrary spin by taking the spin-3 TMHSG action constructed in arXiv:1107.0915 and subsequently generalising it for an arbitrary spin. We find that the final result can be put into a product form which cannot be holomorphically factorised. This is consistent with the expectation of a logarithmic CFT dual for TMHSG with boundary conditions that retain all normalisable modes in the bulk.