Bosonic Fradkin-Tseytlin equations unfolded

TL;DR

This paper investigates an infinite-dimensional extension of the su(k,k) algebra as a candidate for conformal higher spin algebra, analyzing its representations and showing it encodes the Fradkin-Tseytlin equations for all integer spins.

Contribution

It provides a detailed analysis of the su(k,k) extension and demonstrates its capability to encode higher spin equations in an unfolded formulation.

Findings

The algebra encodes Fradkin-Tseytlin equations for all integer spins.

The k=2 case is explicitly analyzed and confirmed.

The representations of the algebra are thoroughly explored.

Abstract

We test infinite-dimensional extension of algebra su(k,k) proposed by Fradkin and Linetsky as the candidate for conformal higher spin algebra. Adjoint and twisted-adjoint representations of su(k,k) on the space of this algebra are carefully explored. For k=2 corresponding unfolded system is analyzed and it is shown to encode Fradkin-Tseytlin equations for the set of all integer spins 1,2,... with infinite multiplicity.