Wigner 6j symbols for SU(N): Symbols with at least two quark-lines

TL;DR

This paper derives explicit formulas for a class of SU(N) Wigner 6j symbols involving two fundamental representations, aiding in the efficient decomposition of SU(N) color structures in quantum chromodynamics.

Contribution

It provides explicit N-dependent formulas for SU(N) Wigner 6j symbols with two quark-lines, advancing the understanding of group invariants in color structure decomposition.

Findings

Explicit formulas for all 6j symbols in the studied class.

Formulas expressed in terms of representation dimensions and N.

First step towards efficient SU(N) color structure decomposition.

Abstract

We study a class of SU(N) Wigner 6j symbols involving two fundamental representations, and derive explicit formulae for all 6j symbols in this class. Our formulae express the 6j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulae as a first step towards efficiently decomposing SU(N) color structures in terms of group invariants.