${\cal N}=2$ supersymmetric higher spin gauge theories and current multiplets in three dimensions

TL;DR

This paper develops new ${ m N}=2$ supersymmetric higher-spin gauge theories in three dimensions, introducing supermultiplets, topological actions, and supercurrent multiplets, with applications to AdS superspace and massive supermultiplets.

Contribution

It introduces conformal higher-spin gauge superfields, constructs Chern-Simons-type actions, and formulates off-shell descriptions of massless and massive higher-spin supermultiplets in ${ m N}=2$ supersymmetry.

Findings

Constructed gauge-invariant topological $BF$-type terms.

Proposed two off-shell formulations for massless higher-spin supermultiplets.

Formulated consistent higher-spin supercurrent multiplets in (1,1) AdS superspace.

Abstract

We describe several families of primary linear supermultiplets coupled to three-dimensional ${\cal N}=2$ conformal supergravity and use them to construct topological $BF$-type terms. We introduce conformal higher-spin gauge superfields and associate with them Chern-Simons-type actions that are constructed as an extension of the linearised action for ${\cal N}=2$ conformal supergravity. These actions possess gauge and super-Weyl invariance in any conformally flat superspace and involve a higher-spin generalisation of the linearised ${\cal N}=2$ super-Cotton tensor. For massless higher-spin supermultiplets in (1,1) anti-de Sitter (AdS) superspace, we propose two off-shell Lagrangian gauge formulations, which are related to each other by a dually transformation. Making use of these massless theories allows us to formulate consistent higher-spin supercurrent multiplets in (1,1) AdS superspace. Explicit examples of such supercurrent multiplets are provided for models of massive chiral supermultiplets. Off-shell formulations for massive higher-spin supermultiplets in (1,1) AdS superspace are proposed.