A classification of local Weyl invariants in D=8

TL;DR

The paper addresses the problem of classifying local Weyl-invariant scalar densities in eight dimensions and thereby completes the local type-B Weyl anomaly inventory in $D=8$. It develops an algebraic framework using a Weyl-covariant derivative ${\cal D}$ and jet-space methods to construct an 18-term basis of Weyl-invariant scalars, then determines the Weyl variation constraints with computer-assisted representation theory to identify all invariants. The main result is the identification of five new Weyl-invariant densities $I_j$ (in addition to the seven known quartic invariants), leading to a complete description of the eight-dimensional Weyl anomalies via ${\cal A}_8=\sum a_j {\cal I}_j$ with scheme-dependent coefficients. This advances conformal geometry and has implications for AdS/CFT and quantum field theories in curved backgrounds by providing a full catalogue of eight-dimensional type-B conformal terms.

Abstract

Following a purely algebraic procedure, we provide an exhaustive classification of local Weyl-invariant scalar densities in dimension D=8.