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

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.

Comments: 39 pages, v2: Old results unchanged. New results and conclusions for cubic vertices for scalar and vector fields and many technical details in Secs.5,6,7 added. Conjecture about interrelations between cubic vertices for conformal fields and massless fields added. Appendices A,B,C and references added

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• The Schouten tensor as a connection in the unfolding of 3D conformal higher-spin fields
• Geometrical structure of Weyl invariants for spin three gauge field in general gravitational background in $d=4$
• Superfield approach to interacting N=2 massive and massless supermultiplets in 3d flat space