General light-cone gauge approach to conformal fields and applications to scalar and vector fields

TL;DR

This paper develops a light-cone gauge formalism for conformal fields in even-dimensional flat space, deriving interaction vertices for scalar and vector fields and exploring their relations to massless field vertices.

Contribution

It introduces a general ordinary-derivative light-cone gauge approach for conformal fields and derives explicit cubic interaction vertices for scalar and vector cases.

Findings

All parity-even cubic vertices for conformal scalar and vector fields are obtained.

Undressed vertices for conformal fields match those of massless fields up to a factor.

Conjectures relate conformal field vertices to massless field vertices in different theories.

Abstract

Totally symmetric arbitrary spin conformal fields propagating in the flat space of even dimension greater than or equal to four are studied. For such fields, we develop a general ordinary-derivative light-cone gauge formalism and obtain restrictions imposed by the conformal algebra symmetries on interaction vertices. We apply our formalism for the detailed study of conformal scalar and vector fields. For such fields, all parity-even cubic interaction vertices are obtained. The cubic vertices obtained are presented in terms of dressing operators and undressed vertices. We show that the undressed vertices of the conformal scalar and vector fields are equal, up to overall factor, to the cubic vertices of massless scalar and vector fields. Various conjectures about interrelations between the cubic vertices for conformal fields in conformal invariant theories and the cubic vertices for massless fields in Poincare invariant theories are proposed.