Conformal Yang-Mills field in (A)dS space

TL;DR

This paper develops second-derivative Lagrangian formulations for conformal Yang-Mills fields in (A)dS spaces of various dimensions, introducing gauge-invariant models with auxiliary and Stueckelberg fields, and explores their symmetry and unitarity properties.

Contribution

It presents new gauge-invariant Lagrangian formulations for conformal Yang-Mills fields in (A)dS space, including generic and decoupled forms, with explicit symmetry and unitarity analysis.

Findings

Formulations include auxiliary and Stueckelberg fields.

Models are non-unitary due to wrong-sign kinetic terms.

Extended gauge algebra simplifies Lagrangian and transformations.

Abstract

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian formulations which we refer to as generic formulation and decoupled formulation. In both formulations, the usual Yang-Mills field is accompanied by additional vector and scalar fields where the scalar fields are realized as Stueckelberg fields. In the generic formulation, the usual Yang-Mills field is realized as a primary field, while the additional vector fields are realized as auxiliary fields. In the decoupled formulation, the usual Yang-Mills field is realized as massless field, while the additional vector fields together with the Stueckelberg are realized as massive fields. Some massless/massive fields appear with the wrong sign of kinetic terms, hence demonstrating explicitly that the considered models are not unitary. The use of embedding space method allows us to treat the isometry symmetries of (A)dS space manifestly and obtain conformal transformations of fields in a relatively straightforward way. By accompanying each vector field by the respective gauge parameter, we introduce an extended gauge algebra. Levy-Maltsev decomposition of such algebra is noted. Use of the extended gauge algebra setup allows us to present concise form for the Lagrangian and gauge transformations of the conformal Yang-Mills field. Higher-derivative representation of the Lagrangian is also obtained.