The conformally invariant symmetric traceless field: a conformal field strength and a conformally invariant gauge fixing equation over (A)dS$_4$
Julien Queva
TL;DR
This work develops a conformally invariant framework for a symmetric traceless field $A^{ abla ext{...} u_s}$ of rank $s$ on conformally flat Einstein spacetimes, introducing the principal equation $E_s(A)=0$ and a conformally invariant gauge fixing in four dimensions. It defines a covariant field strength $F= abla^ ho A^{ ext{...}}$ and proves its gauge invariance and its own conformally invariant equations at $d=4$, including an electromagnetic-like decomposition into $E_j$ and $B_j$ that exhibits duality and an $ ext{so}(2,4)$ action. A restricted Weyl-invariant gauge fixing equation arises from a Branson–GJMS-type factorization in $d=4$, and the $F$-based dynamics admit a conformally invariant action and a gauge-invariant symplectic form, suggesting a path toward quantization of higher-spin conformal fields on CFES. The results unify conformal, gauge, and duality structures for higher-spin traceless fields and provide concrete tools (field strength, first-order systems, EM decomposition) to study their dynamics and quantization in four dimensions. The framework has potential implications for higher-spin conformal theories and generalized conformal gravity on CFES, with explicit connections to Eastwood–Singer-type gauges and Branson’s operators.
Abstract
The conformally invariant symmetric traceless field $A$ is considered. In four dimensions it possesses a scalar gauge invariance to which we provide a conformally invariant gauge fixing equation. A field strength $F$ is built upon $A$, its properties are worked out, giving rise to a set of conformally invariant equations exhibiting an electromagnetic duality.