Appendix A: SU (3) projection In this appendix we describe the two SU (3) projection schemes used in this paper and show their equivalence in the weak coupling limit. Necessary properties of the projector mapping an arbitrary, complex 3 × 3 matrix on the SU (3) subgroup are idempotence and gauge-covariance. These properties are not sufficient to specify a unique projector and hence several choices exist. For APE smearing we use the unit circle projection [46] which is based on polar decomposition, while for HYP smearing we seek iteratively the matrix U$_{max}$ ∈ SU (3) which maximizes Re Tr( U$_{max}$V $^{†}$) [47]. First we describe the unit circle projection [46]. For a complex 3 × 3 matrix V with det( V ) = 0, we calculate the matrix which is unitary by construction and has a spectrum lying on the unit circle. The square root is obtained by Jacobi matrix diagonalization. From W we obtain a special unitary matrix by computing This projection is idempotent since an element of SU (3) is projected by Eqs. (A1) and (A2) back onto itself. The projection is also gauge covariant, as we now show. The matrices V and V † transform as and hence Since [ V $^{†}$V ] − 1 / 2 has the same transformation properties as V $^{†}$V one finds for the transfor- mation of W from which the gauge-covariance of V follows. 45 W → G$_{L}$WG † $_{R}$, (A5) V $^{†}$V → G$_{R}$V $^{†}$V G † $_{R}$. (A4) V → G$_{L}$V G † R and V † → G$_{R}$V $^{†}$G † $_{L}$, (A3) W = V [ V $^{†}$V ] − 1 / $^{2}$, (A1) V = [(det( W )] − 1 / $^{3}$W. (A2)