On \U0001d4a9 = 1, 2, 4 higher spin gauge theories in four dimensions

Abstract

We study \U0001d4a9 = 1, 2, 4 higher spin superalgebras in four dimensions and higher spin gauge theories based on them. We extend the existing minimal \U0001d4a9 = 2, 4 theories and find a minimal \U0001d4a9 = 1 theory. Utilizing the basic structure of the minimal \U0001d4a9 = 8 theory, we express the full field equations for the \U0001d4a9 = 1, 2, 4 theories in a universal form without introducing Kleinian operators. We also use a non-minimal \U0001d4a9 = 4 higher spin algebra tensored with U(3) to describe a higher spin extension of \U0001d4a9 = 4 supergravity coupled to the massless vector multiplets arising in the KK spectrum of 11D supergravity on the \U0001d4a9 = 3 supersymmetric AdS4 × 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 \U0001d4a9 = 4 is broken down to \U0001d4a9 = 3.