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

TL;DR

This paper explores the properties and interactions of non-Abelian tensor gauge fields of second rank, revealing their unique features distinct from gravitons and B fields through theoretical analysis.

Contribution

It provides a detailed analysis of the propagation and interactions of second-rank non-Abelian tensor gauge fields, including Bianchi identities and differential equations, highlighting their novel characteristics.

Findings

Polarizations resemble graviton and B field but differ in interactions

Field strength tensor satisfies Bianchi identity

Propagation described by second-order PDEs

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.