On partition function and Weyl anomaly of conformal higher-spin fields

We study 4-dimensional higher-derivative conformal higher-spin (CHS) fields generalizing Weyl graviton and conformal gravitino. They appear, in particular, as "induced" theories in the AdS/CFT context. We consider their partition function on curved Einstein-space backgrounds like (A)dS or sphere and Ricci-flat spaces. Remarkably, the bosonic (integer spin s) CHS partition function appears to be given by a product of partition functions of the standard 2nd-derivative "partially massless" spin s fields, generalizing the previously known expression for the 1-loop Weyl graviton (s = 2) partition function. We compute the corresponding spin s Weyl anomaly coefficients a(s) and c(s). Our result for as reproduces the expression found recently in arXiv:1306.5242 by an indirect method implied by AdS/CFT (which relates the partition function of a CHS field on S-4 to a ratio of known partition functions of massless higher-spin field in AdS(5) with alternate boundary conditions). We also obtain similar results for the fermionic CHS fields. In the half-integer s case the CHS partition function on (A)dS background is given by the product of squares of "partially massless" spin s partition functions and one extra factor corresponding to a special massive conformally invariant spin s field. It was noticed in arXiv:1306.5242 that the sum of the bosonic as coefficients over all s is zero when computed using the zeta-function regularization, and we observe that the same property is true also in the fermionic case. (C) 2013 Elsevier B.V. All rights reserved.