Determination of SU(4)$_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor

TL;DR

This paper proposes a method to determine the SU(4) technicolor gauge group value by embedding a one-family technicolor model into an extended technicolor theory, providing a novel theoretical approach.

Contribution

It introduces a new technique to fix the technicolor gauge group size based on embedding principles, specifically determining N_TC=4.

Findings

N_TC is deduced to be 4 from the embedding approach.

Provides a theoretical foundation for choosing N_TC in technicolor models.

Enhances understanding of gauge group determination in technicolor theories.

Abstract

In technicolor theories using an SU($N_{TC}$) gauge group, the value of $N_{TC}$ is not, {\it a priori}, determined and is typically chosen by phenomenological criteria. Here we present a novel way to determine $N_{TC}$ from the embedding of a one-family technicolor model, with fermions in the fundamental represention of SU($N_{TC}$), in an extended technicolor theory, and use it to deduce that $N_{TC}=4$ in this framework.