Partition Functions for Higher-Spin theories in AdS

We calculate the one-loop partition function for a massless arbitrary-spin field on quotients of a general dimensional AdS background using the results of arXiv:1103.3627. We use these results to compute the one-loop partition function for a Vasiliev theory in AdS_5. An interesting form of the answer, suggestive of a vacuum character of an enhanced symmetry algebra is obtained. We also observe a close connection between the partition function for this Vasiliev theory and the d-dimensional MacMahon function.