Weyl anomaly of conformal higher spins on six-sphere

TL;DR

The paper computes the six-dimensional Weyl anomaly for conformal higher-spin fields by evaluating the Seeley–DeWitt $B_6$ coefficient for CHS on $S^6$ using a $ abla^2$-type spectral analysis of the transverse traceless operators. It then matches this UV coefficient to the IR divergence $a_s$ obtained from the ratio of massless higher-spin determinants in AdS$_7$, confirming the holographic relation $B^{(s)}_6=-a_s$ and extending the previously established $d=4$ results. An explicit closed-form expression for $a_s$ (and thus $-B^{(s)}_6$) in terms of the spin $s$ is given, along with the analogous massless-spin contribution and a $d=2$ cross-check in the Appendix. The findings strengthen the AdS/CFT-inspired link between CHS Weyl anomalies on the boundary and bulk determinant ratios, and they shed light on the spin-spectrum structure and possible extensions to other backgrounds and formulations of CHS theory in six dimensions.

Abstract

This paper is a sequel to arXiv:1309.0785 were we computed the Weyl anomaly a-coefficient on d-sphere for higher-derivative conformal higher spin field in d=4 and shown that it matches the expression found in arXiv:1306.5242 by a "holographic" method from a ratio of massless higher spin determinants in AdS_5. Here we repeat the same computation on 6-sphere and demonstrate that the result agrees again with the one following from AdS_7. We also discuss explicitly similar matching in the d=2 case.