Infinite (continuous) spin fields in the frame-like formalism

TL;DR

This paper develops a gauge invariant frame-like Lagrangian formalism for infinite (continuous) spin representations of the Poincaré group, extending previous massive field results and exploring solutions in (Anti) de Sitter spaces.

Contribution

It introduces a novel gauge invariant formalism for infinite spin fields, generalizing to (Anti) de Sitter spaces and connecting to previous massive field frameworks.

Findings

Infinite spin solutions constructed as a limit of massive mixed symmetry fields.

No unitary solutions found in de Sitter space.

Existence of a wide spectrum of solutions in Anti de Sitter space.

Abstract

In this paper we elaborate on the gauge invariant frame-like Lagrangian description for the wide class of the so-called infinite (or continuous) spin representations of Poincar\'e group. We use our previous results on the gauge invariant formalism for the massive mixed symmetry fields corresponding to the Young tableau with two rows Y(k,l) (Y(k+1/2,l+1/2) for the fermionic case). We have shown that the corresponding infinite spin solutions can be constructed as a limit where k goes to infinity, while l remain to be fixed and label different representations. Moreover, our gauge invariant formalism provides a natural generalization to (Anti) de Sitter spaces as well. As in the completely symmetric case considered earlier by Metsaev we have found that there are no unitary solutions in de Sitter space, while there exists a rather wide spectrum of Anti de Sitter ones. In this, the question what representations of the Anti de Sitter group such solutions correspond to remains to be open.