Ordinary-derivative formulation of conformal low-spin fields

TL;DR

This paper develops an ordinary-derivative formulation for conformal fields of various spins in flat space, introduces gauge-invariant Lagrangians, and explores their symmetries and applications to Weyl gravity and higher-derivative theories.

Contribution

It presents a novel ordinary-derivative approach for conformal low-spin fields, including gauge-invariant Lagrangians and symmetry realizations, extending the understanding of conformal and Weyl gravity.

Findings

Constructed second-derivative formulations for spin 0,1,2 bosonic fields.

Developed first-derivative formulations for spin 1/2,3/2 fermionic fields.

Connected Weyl gravity with Einstein AdS gravity through symmetry breaking.

Abstract

Conformal fields in flat space-time of even dimension greater than or equal to four are studied. Second-derivative formulation for spin 0,1,2 conformal bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we obtain gauge invariant Lagrangians and the corresponding gauge transformations. Gauge symmetries are realized by involving Stueckelberg fields and auxiliary fields. Realization of global conformal boost symmetries is obtained. Modified Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the field content of Weyl gravity, in addition to conformal graviton field, includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg vector field. With respect to the auxiliary tensor field, the Lagrangian contains, in addition to other terms, the Pauli-Fierz mass term. Using the ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries. Also, we demonstrate use of the light-cone gauge for counting on-shell degrees of freedom in higher-derivative conformal field theories.