Bosonic Fradkin-Tseytlin equations unfolded. Irreducible case

TL;DR

This paper constructs a family of irreducible modules for 4d conformal algebra, leading to unfolded equations that describe all spins in the Fradkin-Tseytlin system, generalizing higher spin conformal theories.

Contribution

It introduces a new class of irreducible modules parameterized by a real number, providing a unified unfolded formulation for all spins in 4d conformal higher spin theory.

Findings

Constructed irreducible modules $M_\alpha$ for 4d conformal algebra.

Derived unfolded equations for all spins $s=1,\dots,\infty$.

Showed independence of equations from parameter $\alpha$.

Abstract

We factorize 4d Fradkin-Linetsky higher spin conformal algebra by maximal ideal $I^1-\alpha$ and construct irreducible infinite-dimensional modules $M_\alpha$ of 4d conformal algebra that are parameterized by real number $\alpha$. It is shown that independently of $\alpha$ unfolded system of equations corresponding to each $M_\alpha$ describes collection of Fradkin-Tseytlin equations for all spins $s=1,\dots,\infty$ with zero multiplicity.