Infinite Spin Fields in d = 3 and Beyond

Yurii Zinoviev

doi:10.3390/universe3030063

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 field, leaving the sum of their Lagrangians invariant. Properties of such fields and supermultiplets in four and higher dimensions are also briefly discussed.

Highlights

Besides the very well known finite-component massless and massive representations of the Poincare algebra, there are rather exotic so-called infinite spin representations
One of the reasons is that, contrary to the finite-component massless fields, such representations are characterized by a dimensionful parameter and so they may provide an interesting alternative for the massless higher spin theory in the flat space
We have seen that the same frame-like gauge-invariant formalism that has been developed for the description of massive higher spin fields can be successfully applied to the massless infinite spin case as well providing an explicit realization for the general idea that massless infinite spin representations can be obtained as an appropriate limit from the massive ones

Summary

Introduction

Besides the very well known finite-component massless and massive representations of the Poincare algebra, there are rather exotic so-called infinite (or continuous) spin representations (see e.g., [1,2]). One of the reasons is that, contrary to the finite-component massless fields, such representations are characterized by a dimensionful parameter (that can play the same role as the cosmological constant for the massless theories and the mass for the massive ones) and so they may provide an interesting alternative for the massless higher spin theory in the flat space. Note that such representations can appear in the tensionless limit of the string theory. We develop the frame-like formalism for the massless infinite spin bosonic and fermionic fields as well as for the supermultiplet containing such fields

Infinite Spin Boson

Fermionic Case

Infinite Spin Supermultiplet

Conclusions