QG seminar: Spin-(s,j) projectors and gauge-invariant spin-s actions in maximally symmetric backgrounds

QG unit Zoom seminar.
Speaker: Daniel Hutchings (University of Western Australia).
Title: Spin-(s,j) projectors and gauge-invariant spin-s actions in maximally symmetric backgrounds.

Spin projection operators have found numerous applications within the landscape of higher- spin theory, such as in the construction of (i) massive spin-s propagators; (ii) conformal spin-s actions; and (iii) massive spin-s actions with s ≤ 4. These projectors are members of the less well-known family of operators known as the spin-(s,j) projection operators, which until recently, had only been computed in four-dimensional Minkowski space over 50 years ago. It is well known that on such a background, a symmetric and traceless rank-s field satisfying the massive Klein-Gordon equation furnishes a collection of massive representations of the Poincaré algebra with spins j ∈ {0, 1, · · · , s}. The role of the spin-(s, j) projector is to isolate the part of these fields that furnishes the representation from this collection carrying spin j. In this talk, I will discuss recent advancements in the study of these projectors, including an extension to d-dimensional maximally symmetric backgrounds, and explore some of their applications. In particular, we show that they facilitate a systematic derivation of two-derivative actions with a propagating massless spin-s mode.