  We study the one-loop renormalisation of 4d SU(N) Yang-Mills theory with $M$
adjoint representation scalar multiplets. We calculate the coupled one-loop
renormalization group flows for this theory by developing an algebraic
description, which we find to be characterised by a non-associative algebra of
marginal couplings. The 4d one-loop beta function of the gauge coupling $g^2$
vanishes for the case $M = 22$, which is intriguing for string theory. There
are real fixed flows (fixed points of $\lambda/g^2$) only for $M\geq406$,
rendering one-loop fixed points of the gauge coupling and scalar couplings
incompatible.
