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

Abstract

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