On the realization of infinite (continuous) spin field representations in AdS${}_{\mathbf{4}}$ space

TL;DR

This paper investigates the symmetry properties of infinite spin fields in AdS4 space, demonstrating their invariance under SO(2,3) and characterizing their representation structure within a specific Lagrangian model.

Contribution

It provides a detailed analysis of the symmetry constraints and representation classification of infinite spin fields in AdS4, extending understanding of their algebraic and geometric properties.

Findings

Infinite spin states are SO(2,3)-invariant.

Casimir operators are fixed by constraints, with only one independent.

Infinite spin fields correspond to the most degenerate SO(2,3) representations.

Abstract

We study the symmetry properties of infinite spin fields in $\rm{AdS}_4$ space which are involved in the Lagrangian model proposed in arXiv:2403.14446 where the main role is played by operator constraints. It is shown that the conditions defining infinite spin states in $\rm{AdS}_4$ space are $\mathrm{SO}(2,3)$-invariant. It is found that in the model under consideration the Casimir operators are completely fixed by the constraint operators and only one of the Casimir operators is independent. It is shown that in this model, infinite spin fields in $\rm{AdS}_4$ space are described by the most degenerate representations of the $\mathrm{SO}(2,3)$ group.