Non-Abelian Tensors with Consistent Interactions

TL;DR

This paper introduces a systematic method for constructing consistent interactions for arbitrary rank tensor fields in gauge theories, utilizing dimensional reduction and Chern-Simons modifications to ensure consistency.

Contribution

It provides a new framework for defining consistent field strengths and gauge transformations for high-rank tensors in arbitrary gauge groups and dimensions.

Findings

Developed a multiplet structure for tensor fields to ensure consistency.

Modified field strengths with Chern-Simons forms to maintain gauge invariance.

Circumvented traditional consistency problems in tensor field equations.

Abstract

We present a systematic method for constructing consistent interactions for a tensor field of an arbitrary rank in the adjoint representation of an arbitrary gauge group in any space-time dimensions. This method is inspired by the dimensional reduction of Scherk-Schwarz, modifying field strengths with certain Chern-Simons forms, together with modified tensorial gauge transformations. In order to define a consistent field strength of a r-rank tensor B_{\mu_1...\mu_r}^I in the adjoint representation, we need the multiplet (B_{\mu_1...\mu_r}^I, B_{\mu_1...\mu_{r-1}}^{I J}, ..., B_\mu^{I_1...I_r}, B^{I_1... I_{r+1}}). The usual problem of consistency of the tensor field equations is circumvented in this formulation.