Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>D</a:mi><a:mo>></a:mo><a:mn>4</a:mn></a:math>, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi><c:mo>=</c:mo><c:mn>4</c:mn></c:math>, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>D</e:mi><e:mo>=</e:mo><e:mn>4</e:mn></e:math>, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024