Off-shell higher spin N=2 supermultiplets in three dimensions

Abstract

Off-shell higher spin N=2 supermultiplets in three spacetime dimensions (3D) are presented in this paper. We propose gauge prepotentials for higher spin superconformal gravity and construct the corresponding gauge-invariant field strengths, which are proved to be conformal primary superfields. These field strengths are higher spin generalisations of the (linearised) N=2 super-Cotton tensor, which controls the superspace geometry of conformal supergravity. We also construct the higher spin extensions of the linearised N=2 conformal supergravity action. We provide two dually equivalent off-shell formulations for massless higher spin N=2 supermultiplets. They involve one and the same superconformal prepotential but differ in the compensators used. For the lowest superspin value 3/2, these higher spin series terminate at the linearised actions for the (1,1) minimal and w=-1 non-minimal N=2 Poincaré supergravity theories constructed in arXiv:1109.0496. Similar to the pure 3D supergravity actions, their higher spin counterparts propagate no degrees of freedom. However, the massless higher spin supermultiplets are used to construct off-shell massive N=2 supermultiplets by combining the massless actions with those describing higher spin extensions of the linearised N=2 conformal supergravity. We also demonstrate that every higher spin super-Cotton tensor can be represented as a linear superposition of the equations of motion for the corresponding massless higher spin supermultiplet,with the coefficients being higher-derivative linear operators.