Cubic Vertices for N=1 Supersymmetric Massless Higher Spin Fields in Various Dimensions

TL;DR

This paper develops a BRST-based method to construct cubic interaction vertices for N=1 supersymmetric massless higher spin fields across various dimensions, revealing supersymmetry constraints and specific solutions.

Contribution

It introduces a generic technique for deriving cubic vertices for higher spin fields in multiple dimensions, incorporating supersymmetry constraints and applications to Yang-Mills-like and supergravity-like systems.

Findings

Supersymmetry imposes additional constraints on cubic vertices.

Explicit solutions for vertices with off-shell constraints are provided.

The method applies to four, six, and ten-dimensional theories.

Abstract

Using the BRST approach to higher spin field theories we develop a generic technique for constructing the cubic interaction vertices for N=1 supersymmetric massless higher spin fields on four, six and ten dimensional flat backgrounds. Such an approach allows formulation of the equations for cubic vertices including bosonic and fermionic higher spin fields, and the problem of finding the vertices is reduced to finding the consistent solutions to these equations. As a realization of this procedure, we present the particular solutions for the vertices where the fields obey some off-shell constraints. It is shown that the supersymmetry imposes additional constraints on the vertices and singles out a particular subclass of the solutions. As a concrete application of the generic scheme, we consider supersymmetric Yang-Mills-like systems in four, six and ten dimensions where the higher spin fields transform under some internal symmetry group, as well as supergravity-like systems in the same dimensions.