Abstract
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.
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