A generating function for the cubic interactions of higher spin fields

TL;DR

The paper advances higher-spin theory by providing an off-shell generating function for all cubic interactions of HS gauge fields, extending the previously known on-shell generating function. It introduces a compact generating form $\\mathcal{A}$ and an operator $\\hat{W}$, augmented with Grassmann variables, to generate all couplings for spins $s_{1},s_{2},s_{3}$ with derivative counts $\\Delta$ in $\\Delta_{\\min}\\le\\Delta\\le\\Delta_{\\max}$; two equivalent realizations of $\\hat{W}$ yield the same Lagrangian up to integration by parts and field redefinitions. The construction reproduces GTI results in flat space and relates to the Sagnotti–Taronna on-shell generating function, offering a universal off-shell framework and a route to higher-order (quartic) interactions and potential string-theory connections. The approach highlights a remarkable structural simplicity and a Grassmann-augmented method that compactly encodes all cubic couplings across arbitrary HS spins.

Abstract

We present an off-shell generating function for all cubic interactions of Higher Spin gauge fields constructed in arXiv:1003.2877. It is a generalization of the on-shell generating function proposed in arXiv:1006.5242, is written in a very compact way, and turns out to have a remarkable structure.