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

Abstract

We describe several families of primary linear supermultiplets coupled to three-dimensional $\mathcal{N}=2$ 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 $\mathcal{N}=2$ conformal supergravity. These actions possess gauge and super-Weyl invariance in any conformally flat superspace and involve a higher-spin generalisation of the linearised $\mathcal{N}=2$ 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.

48 pages; v2: comments and references added. arXiv admin note: text overlap with arXiv:1805.08055

References in corpus (11)

• Off-shell massive N=1 supermultiplets in three dimensions
• Off-shell superconformal nonlinear sigma-models in three dimensions
• Three-dimensional (p,q) AdS superspaces and matter couplings
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• Higher spin supercurrents in anti-de Sitter space
• Conserved higher spin supercurrents for arbitrary spin massless supermultiplets and higher spin superfield cubic interactions
• The massless integer superspin multiplets revisited
• Higher Spin Superfield interactions with Complex linear Supermultiplet: Conserved Supercurrents and Cubic Vertices
• Higher Spin Superfield interactions with the Chiral Supermultiplet: Conserved Supercurrents and Cubic Vertices
• Higher spin supermultiplets in three dimensions: (2,0) AdS supersymmetry
• Supersymmetric Spacetimes from Curved Superspace

Cited by in corpus (11)

• Progress on cubic interactions of arbitrary superspin supermultiplets via gauge invariant supercurrents
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• Extended superconformal higher-spin gauge theories in four dimensions
• Higher spin supermultiplets in three dimensions: (2,0) AdS supersymmetry
• Hierarchy of Supersymmetric Higher Spin Connections
• Linearised actions for $\mathcal{N}$-extended (higher-spin) superconformal gravity
• Field theories with (2,0) AdS supersymmetry in $\mathcal{N}=1$ AdS superspace
• Superspace First Order Formalism, Trivial Symmetries and Electromagnetic Interactions of Linearized Supergravity
• Lagrangian formulation of free arbitrary N-extended massless higher spin supermultiplets in 4D, AdS space
• Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$: Reduction to (1,0) superspace
• Superspace First-order Formalism for Massless Arbitrary Superspin Supermultiplets