Flavour singlets in gauge theory as Permutations

Understand

Gauge-invariant operators can be specified by equivalence classes of permutations.

• We develop this idea concretely for the singlets of the flavour group $SO(N_f)$ in $U(N_c)$ gauge theory by using Gelfand pairs and Schur-Weyl duality.
• The singlet operators, when specialised at $N_f =6$, belong to the scalar sector of ${\cal N}=4$ SYM.
• A simple formula is given for the two-point functions in the free field limit of $g_{YM}^2 =0$.