Off-shell higher-spin gauge supermultiplets and conserved supercurrents

TL;DR

This thesis develops new off-shell formulations for higher-spin supermultiplets and supercurrents in various supersymmetric theories, providing explicit constructions and extending the understanding of supersymmetric higher-spin gauge theories in different spacetime dimensions and backgrounds.

Contribution

It introduces novel off-shell formulations for massless higher-spin supermultiplets and supercurrents in 3D and 4D superspaces, including first-time constructions for certain multiplets.

Findings

Explicit supercurrent expressions in 4D Minkowski and AdS superspaces.

New off-shell formulations for massless higher-spin multiplets in 3D AdS.

Construction of massive ${ m N}=1$ gravitino supermultiplet models.

Abstract

This thesis presents the general structure of non-conformal higher-spin supercurrent multiplets in three and four spacetime dimensions. Such supercurrents are in one-to-one correspondence with off-shell massless higher-spin gauge supermultiplets, some of which are constructed in this thesis for the first time. In the first part of the thesis, we propose a new off-shell formulation for a massless integer superspin multiplet, whose gauge-invariant action involves an unconstrained complex superconformal prepotential, in conjunction with two types of compensators. Next, we deduce the structure of consistent non-conformal higher-spin ${\cal N}=1$ supercurrents. Explicit expressions for such supercurrents are derived for various theories in 4D ${\cal N}=1$ Minkowski and AdS superspaces. These include a model of $N$ massive chiral superfields with an arbitrary mass matrix, along with free theories of tensor and complex linear superfields. The second part of the thesis is devoted to ${\cal N}=1$ and ${\cal N}=2$ supersymmetric higher-spin theories in 3D AdS space. Two dually equivalent off-shell Lagrangian formulations for the massless multiplets of arbitrary superspin in (1,1) AdS superspace and their corresponding supercurrents are derived. With regards to (2,0) AdS supersymmetry, we identify a multiplet of conserved higher-spin currents in models for a chiral superfield, which is then used to construct two series of a massless half-integer superspin multiplet. Finally, our (2,0) AdS supermultiplets are reduced to (1,0) AdS superspace, yielding four series of ${\cal N}=1$ supersymmetric higher-spin models. Further applications of these massless models are discussed, one of which is related to the construction of two new off-shell formulations for the massive ${\cal N}=1$ gravitino supermultiplet in AdS.