Propagating modes of a non-Abelian tensor gauge field of second rank

Abstract

In the recently proposed extension of the YM theory, non-Abelian tensor gauge field of the second rank is represented by a general tensor whose symmetric part describes the propagation of charged gauge boson of helicity two and its antisymmetric part -the helicity zero charged gauge boson. On the non-interacting level these polarizations are similar to the polarizations of the graviton and of the Abelian antisymmetric B field, but the interaction of these gauge bosons carrying non-commutative internal charges cannot be directly identified with the interaction of gravitons or B field. Our intention here is to illustrate this result from different perspectives which would include Bianchi identity for the corresponding field strength tensor and the analysis of the second-order partial differential equation which describes in this theory the propagation of non-Abelian tensor gauge field of the second rank. Analyzing the interaction between two tensor currents caused by the exchange of these tensor gauge bosons we shall demonstrate that the residue at the pole is the sum of three terms each of which describes positive norm polarizations of helicities two and zero bosons.

Extended gauge theory and gauged free differential algebras

“…In other words, we show that the above mentioned non abelian gauge theory, where the gauge fields are described by p-forms with p ≥ 2, can be obtained by gauging free differential algebras. * Electronic address: pasalgad@udec.cl † Electronic address: sesalgado@udec.cl Higher gauge theory [1][2][3][4][5][6][7][8] is an extension of ordinary gauge theory, where the gauge potentials and their gauge curvatures are higher degree forms. It is believed that higher gauge theories describe the dynamics of higher dimensional extended objects thought to be the basic building blocks of fundamental interactions.The basic field of the abelian higher gauge theory, originated in supergravity, is a pform gauge potential A whose (p + 1)-form curvature is given by F = dA from which the Lagrangian and the action of the theory can be constructed.…”

“…However, for higher dimensional submanifolds such a canonical order is not available.This lack of natural order led to C. Teitelboim in Ref.[9] to the formulation of a no-go theorem, ruling out the existence of non-abelian gauge theories for extended objects.Recent attempts to circumvent this theorem has been carried out in Refs. [1][2][3][4][5][6][7][8]. In particular, in Refs.…”

“…Recent attempts to circumvent this theorem has been carried out in Refs. [1][2][3][4][5][6][7][8]. In particular, in Refs.…”

Topological mass generation four-dimensional gauge theory

“…Let us shortly overview the helicity content of the massless tensor gauge fields before including a massive term into the Lagrangian [21,22,23,31,32].…”

“…where ξ a λ and ζ a µ are gauge parameters. This free equation describes the propagation of massless modes of helicity-two and helicity-zero, λ = ±2, 0, charged gauge bosons [21,22,23,31,32]. This can be seen by decomposition of the rank-2 gauge field into symmetric A S µλ and antisymmetric parts B µλ .…”