Higher spin super-Cotton tensors and generalisations of the linear–chiral duality in three dimensions

In three spacetime dimensions, (super)conformal geometry is controlled by the (super-)Cotton tensor. We present a new duality transformation for N -extended supersymmetric theories formulated in terms of the linearised super-Cotton tensor or its higher spin extensions for the cases N = 2 , 1 , 0 . In the N = 2 case, this transformation is a generalisation of the linear–chiral duality, which provides a dual description in terms of chiral superfields for general models of self-interacting N = 2 vector multiplets in three dimensions and N = 1 tensor multiplets in four dimensions. For superspin-1 (gravitino multiplet), superspin-3/2 (supergravity multiplet) and any higher superspin s ≥ 2 , the duality transformation relates a higher-derivative theory to one containing at most two derivatives at the component level. In the N = 1 case, we introduce gauge prepotentials for higher spin superconformal gravity and construct the corresponding super-Cotton tensors, as well as the higher spin extensions of the linearised N = 1 conformal supergravity action. Our N = 1 duality transformation is a higher spin extension of the known superfield duality relating the massless N = 1 vector and scalar multiplets. Our N = 0 duality transformation is a higher spin extension of the vector-scalar duality.