Infinite spin fields in d = 3 and beyond

Abstract: In this paper we consider the frame-like formulation for the so called infinite (continuous) spin representations of the Poincare algebra. In the three dimensional case we give explicit Lagrangian formulation for bosonic and fermionic infinite spin fields (including the complete sets of the gauge invariant objects and all the necessary extra fields). Moreover we find the supertransformations for the supermultiplet containing one bosonic and one fermionic fields leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed.