point and all the conclusion of that paper would still hold even if the arbitrary cutoff $\Lambda$ is kept.

The conclusion of [@Conlon:2009xf] (see also [@Conlon:2009kt]) however depends crucially on the choice $\Lambda=M_{P}$. With this the argument of the log in the second term of the is $$\frac{\Lambda^{2}{\cal V}^{-2/3}}{\mu^{2}}\rightarrow\frac{M_{P}^{2}{\cal V}^{-2/3}}{\mu^{2}}\simeq\frac{M_{string}^{2}R^{2}}{\mu^{2}},\label{eq:conlon}$$ where we’ve used (the approximate) formula $M_{string}^{2}\simeq M_{P}^{2}/{\cal V}$ and put $R\equiv{\cal V}^{1/6}$ the size of the internal space in string units. From this it is concluded that the effective unification scale (for large volume compactifications) can be far above the string scale[^5]. As the authors themselves point out in a footnote it is not clear what the “operational” meaning of this is. Clearly it cannot have any, for if instead of the above choice of $\Lambda=M_{P}$ we took a fixed value of $\Lambda\lesssim M_{string}$ (as one should)[^6], then the corresponding unification scale would be below the string scale! However in [@Conlon:2009kt] the authors go on to derive physical conclusions based on having a cutoff that is larger than the string scale.

These come from the authors’ comparison of (after replacing $\Lambda\rightarrow M_{P}$) with a string theory calculation. Based on a background expansion of the sort that we discussed in 