Circumventing the No-Go Theorem in Noncommutative Gauge Field Theory

TL;DR

This paper extends the noncommutative gauge field theory framework to bypass a no-go theorem, enabling more flexible model building with multiple gauge group factors and broader representations.

Contribution

It introduces a method using half-infinite Wilson lines to construct tensor representations for arbitrary products of $U_*(N)$ groups, overcoming previous restrictions.

Findings

Extended noncommutative tensor representations for multiple gauge groups.

Allowed representations beyond the no-go theorem constraints.

Facilitated the construction of more realistic particle interaction models.

Abstract

Stringent restrictions for model building are imposed by a no-go theorem in noncommutative gauge field theory. Circumventing this theorem is crucial for the construction of realistic models of particle interactions. To this end, the noncommutative construction of tensor representations of gauge groups using half-infinite Wilson lines is extended to allow for gauge groups consisting of an arbitrary number of $U_*(N)$ factors. This as well allows representations other than the ones permitted by the no-go theorem.