We find a simple relation between a free higher spin partition function on the thermal quotient of and the partition function of the associated d -dimensional conformal higher spin field defined on the thermal quotient of . Starting with a conformal higher spin field defined in , one may also associate to with another conformal field in dimensions, thus iterating AdS/CFT. We observe that in the case of , this iteration leads to a trivial 3d higher spin conformal theory with parity-even non-local action: it describes a zero total number of dynamical degrees of freedom and the corresponding partition function is equal to 1.
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Beccaria et al. (2016) studied this question.
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