Effective action for conformal spins on spheres with the multiplicative and conformal anomalies

TL;DR

This paper evaluates multiplicative anomalies for conformal higher spin operators on spheres, computes determinants explicitly using zeta functions, and derives conformal anomalies across various spins and dimensions.

Contribution

It provides explicit calculations of determinants and anomalies for conformal higher spins on spheres, extending previous work with new explicit formulas and anomaly results.

Findings

Explicit determinant formulas in terms of zeta functions

Identification of multiplicative anomalies for higher spin operators

Conformal anomaly results for arbitrary spin and dimension

Abstract

Two multiplicative anomalies are evaluated for the determinant of the conformal higher spin propagating operator on spheres given by Tseytlin. One holds for the decomposition of the higher derivative product into its individual second order factors and the other applies to its complete linear factorisation. Using this last factorisation, I also calculate the determinant explicitly in terms of the Riemann zeta function, for both even and odd dimensions. In the latter case there is no anomaly of course. The conformal anomaly is also found for arbitrary spin and dimension.