On N=1,2,4 Higher Spin Gauge Theories in Four Dimensions

TL;DR

This paper explores the structure and equations of N=1,2,4 higher spin superalgebras and gauge theories in four dimensions, extending previous models and connecting to supergravity and compactification spectra.

Contribution

It introduces a minimal N=1 higher spin theory, expresses field equations in a universal form, and links higher spin extensions to supergravity and super-Higgs mechanisms.

Findings

Extended minimal N=2,4 theories to N=1

Expressed field equations without Kleinian operators

Connected higher spin theories to supergravity spectra

Abstract

We study N=1,2,4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal N=2,4 theories and find a minimal N=1 theory. Utilizing the basic structure of the minimal N=8 theory, we express the full field equations for the N=1,2,4 theories in a universal form without introducing Kleinian operators. We also use a non-minimal N=4 higher spin algebra tensored with U(3) to describe a higher spin extension of N=4 supergravity coupled to the massless vector multiplets arising in the KK spectrum of 11D supergravity on the N=3 supersymmetric AdS_4 x N^{010} background. The higher spin theory also contains a triplet of vector multiplets which may play a role in the super-Higgs effect in which N=4 is broken down to N=3.