= Integer obstruction to one-loop marginality with adjoint Dirac fermions
For a non-Abelian simple gauge factor with $C_A>0$, pure <Yang-Mills theory> contributes $-11C_Ag^3/[3(4\pi)^2]$. Adding $N_D$ adjoint <Dirac spinors> changes this to $-C_A(11-4N_D)g^3/[3(4\pi)^2]$. Vanishing would require $N_D=11/4$, which is not a nonnegative integer. This excludes cancellation by these fermions alone, apart from the trivial value $g=0$; other matter representations or fields change the coefficient.
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