What is the mistake of Papadodimas and Raju?

Question

in previously published work of papadodimas and raju, we have taken $O_1 \sim 4\pi$. this is an embarrasing mistake but because $\frac{O_1}{O_2}$ is not of the character of a function of $O_1$, we can say that

$O_1 \sim 4\pi(c^2 + \frac{w}{c}\lambda + \frac{c}{2\pi w}(1 + \lambda + \lambda^2 + ...)$

the operators $O^1$ and $O^2$ are near expansion limits of $\frac{c}{(z - w)^2}$. ref bari claims that therefore, the dimensionality of spacetime is not of the character of a OPE singluarity. it can be fixed near 4 or 10, because the OPE is

$\sim \frac{c}{(z - w)^2} + \frac{\frac{c}{w}}{(z - w)^4}$

we have asked ref to share the formula for dimensionality 4 of spacetime, but he has refused.

Comments

we have shown how to renormalize $\phi^4$ theory this essentially depends on the fact that the Lagrangian

$  L  = \frac{1}{2} (\partial \phi) (\partial \phi) + \frac{\phi^4}{\lambda} + series \ 1 + \lambda + \lambda^2 + . . $

renormalizes in both parameters $\lambda$ and a

if we postualte the equivalence of the series

$\frac{c}{2\pi w} log(\frac{\lambda'}{\lambda}) = 1 + \lambda + \lambda^2 + ...$

and 

$log(\frac{\lambda'}{\lambda}) = \lambda + \frac{\lambda^2}{w} + \lambda^3 + \lambda^4 + . . .$

the renormalizability of QCD is demonstrated. perhaps this is known to veltman, in some sense, but 't hooft's article shows only that the coefficient of $\lambda^4$ is

which is $\frac{\alpha}{4\pi}$ in appropriate units. the actual number corresponding to this series is

$\frac{\alpha}{4\pi}(1 + log(\frac{\lambda'}{\lambda} + \frac{log(\frac{\lambda'}{\lambda})}{\beta} + \frac{\beta^2}{2} + . . .)$