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We study the one-loop renormalisation of 4d SU(N) Yang-Mills theory with $M$adjoint representation scalar multiplets. We calculate the coupled one-looprenormalization group flows for this theory by developing an algebraicdescription, which we find to be characterised by a non-associative algebra ofmarginal 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. Thereare real fixed flows (fixed points of $\lambda/g^2$) only for $M\geq406$,rendering one-loop fixed points of the gauge coupling and scalar couplingsincompatible.

One-loop RG Flow for Adjoint Multiscalar Gauge Theory