  We study the one loop renormalisation of 4d $SU(N)$ Yang-Mills theory with
$M$ adjoint representation scalar multiplets related by $O(M)$ symmetry.
General $M$ are of field theoretic interest, and the 4d one loop beta function
of the gauge coupling $g^2$ vanishes for the case $M=22$, which is intriguing
for string theory. This case is related to D3 branes of critical bosonic string
theory in $D=22+4=26$. An RG fixed point could have provided a definition for a
purely bosonic AdS/CFT, but we show that scalar self-couplings $\lambda$ ruin
one-loop conformal invariance in the large $N$ limit. There are real fixed
flows (fixed points of $\lambda/g^2$) only for $M\ge 406$, rendering one-loop
fixed points of the gauge coupling and scalar couplings incompatible.
  We develop and check an algebraic approach to the one-loop renormalisation
group which we find to be characterised by a non-associative algebra of
marginal couplings. In the large $N$ limit, the resulting RG flows typically
suffer from strong coupling in both the ultraviolet and the infrared. Only for
$M\ge 406$ fine-tuned solutions exist which are weakly coupled in the infrared.
