Abstract
This paper is mainly concerned with the construction of new off-shell higher spin N=1 supermultiplets in three spacetime dimensions. We elaborate on the gauge prepotentials and linearised super-Cotton tensors for higher spin N=1 superconformal geometry and propose compensating superfields required to formulate off-shell massless higher spin supermultiplets. The corresponding gauge-invariant actions are worked out explicitly using an auxiliary oscillator realisation. We construct, for the first time, off-shell massive higher spin supermultiplets. The gauge-invariant actions for these supermultiplets are obtained by adding Chern–Simons like mass terms (that is, higher spin extensions of the linearised action for N=1 conformal supergravity) to the actions for the massless supermultiplets. For each of the massive gravitino and supergravity multiplets, we propose two dually equivalent formulations.
Highlights
In three spacetime dimensions (3D), the off-shell structure of N = 1 supergravity was understood in the late 1970s [1, 2, 3] and further elaborated in [4]
There have appeared a number of important developments in minimal 3D supergravity, including the N = 1 topologically massive supergravity with and without a cosmological term [5, 6], various approaches to N = 1 conformal supergravity [7, 8, 9, 10, 11, 12], 3D compactifications of M-theory with minimal local supersymmetry, and higher-derivative models for massive N = 1 supergravity [14, 15, 16, 17]
The latter locally supersymmetric theories, which generalise the models for massive gravity proposed in [18, 19], possess remarkable properties such as unitarity in the presence of curvature squared terms
Summary
Our paper is a continuation of the recent work [24] in which the off-shell massive higher spin N = 2 supermultiplets were constructed in three dimensions The structure of these 3D N = 2 massive supermultiplets is similar to that of the off-shell 4D N = 1 massless supermultiplets [25, 26] (see [27] for a review) in the sense that there are two dually equivalent series of off-shell formulations. The material in subsection 2.1 is taken almost verbatim from [24]
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