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

TL;DR

Overview of 4D ${ m N}=1,2,4$ higher spin gauge theories derived from the maximal ${ m N}=8$ framework, with a Kleinian-free universal master-field formulation. The paper determines spectra from singleton bilinears, constructs minimal and non-minimal algebras with flavor symmetries, and derives full Vasiliev-type field equations along with consistent truncations. A central application to M-theory on ${AdS}_4 imes N^{010}$ yields a matter-coupled ${ m N}=4$ higher spin theory whose spectrum matches KK content and whose higher spin symmetries can break to ${ m N}=3$ via a Higgs-like mechanism. The work provides a holographic setup for free 3D SCFTs with reduced supersymmetry and flavor structure, clarifying the role of flavor multiplets and vector triplets in higher spin dynamics.

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.

Figures (1)

• Figure 1: The arrows denote consistent truncations of higher spin gauge theories described in detail in Section 7.