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Iterating free-field AdS/CFT: higher spin partition function relations

We find a simple relation between a free higher spin field partition function on thermal quotient of AdS(d+1) and the partition function of the associated d-dimensional conformal higher spin field on thermal quotient of AdS(d). Starting with a conformal higher spin field defined on AdS(d) one may also associate to it another conformal field in d-1 dimensions, thus "iterating" AdS/CFT. We observe that in the case of d=4 this iteration leads to a "trivial" 3d higher spin conformal theory with parity-even non-local action: it describes zero total number of dynamical degrees of freedom and the corresponding partition function on thermal AdS(3) is equal to 1.

preprint2016arXivOpen access
M. BeccariaA. A. Tseytlin
hep-th
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M. BeccariaA. A. Tseytlin

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