Conformal Yang-Mills field in arbitrary dimensions

TL;DR

This paper develops a second-derivative, gauge-invariant Lagrangian formulation for conformal Yang-Mills fields in even dimensions, introducing auxiliary fields and deriving higher-derivative actions through field elimination.

Contribution

It presents a novel ordinary-derivative approach to conformal Yang-Mills fields in arbitrary even dimensions, including explicit gauge-invariant Lagrangians and the structure of gauge symmetries.

Findings

Constructed gauge-invariant Lagrangian with second derivatives

Derived FFF-vertex involving three derivatives

Obtained higher-derivative actions by eliminating auxiliary fields

Abstract

Lagrangian of a classical conformal Yang-Mills field in the flat space of even dimension greater than or equal to six involves higher derivatives. We study Lagrangian formulation of the classical conformal Yang-Mills field by using ordinary-derivative (second-derivative) approach. In the framework of the ordinary-derivative approach, a field content, in addition to generic Yang-Mills field, consists of auxiliary vector fields and Stueckelberg scalar fields. For such field content, we obtain a gauge invariant Lagrangian with the conventional second-derivative kinetic terms and the corresponding gauge transformations. The Lagrangian is built in terms of non-abelian field strengths. Structure of a gauge algebra entering gauge symmetries of the conformal Yang-Mills field is described. FFF-vertex of the conformal Yang-Mills field which involves three derivatives is also obtained. For six, eight, and ten dimensions, eliminating the auxiliary vector fields and gauging away the Stueckelberg scalar fields, we obtain a higher-derivative Lagrangian of the conformal Yang-Mills field. For arbitrary dimensions, we demonstrate that all auxiliary fields can be integrated out at non-linear level leading just to a local higher-derivative action which is expressed only in terms of the generic Yang-Mills field.