A Calculus for Higher Spin Interactions

TL;DR

This paper unifies different approaches to higher spin theories using conformal geometry and tractor calculus, providing a generating function for various three-point interactions.

Contribution

It introduces a unified framework combining St"uckelberg and projective space methods via conformal geometry for higher spin interactions.

Findings

Derived a generating function for higher spin three-point interactions.

Unified massless, massive, and partially massless cases in a single framework.

Enhanced understanding of higher spin couplings in conformal geometry.

Abstract

Higher spin theories can be efficiently described in terms of auxiliary St\"uckelberg or projective space field multiplets. By considering how higher spin models couple to scale, these approaches can be unified in a conformal geometry/tractor calculus framework. We review these methods and apply them to higher spin vertices to obtain a generating function for massless, massive and partially massless three-point interactions.