hand the coefficient matrix $\alpha_{ai}\ne0$ only for the index values $i$ corresponding to the the 4-cycles/dell Pezzo surfaces on which the standard model 7-branes are wrapped. In the particular examples that are relevant here, with D3 branes at a singularity, the relevant cycles shrink to a singularity.

In [@Conlon:2009xf] the cutoff $\Lambda$ is taken to be $M_{P}$. As we discussed before there is no physical significance in the actual value of this cut off as long as it is taken to be independent of the moduli. It is simply the upper limit from which one expects the RG evolution to start, and if the field theory is a low energy effective theory whose UV completion is string theory then this scale must necessarily be less than the string scale. As discussed in [@Kaplunovsky:1995jw], for the purpose of comparing the moduli dependence of this formula to that coming from string theory, it does not matter at what point $\Lambda$ is chosen (as long as it is above all low energy thresholds) and indeed without loss of generality it can be chosen to be $M_{P}$. This obviously does not imply any statement about the validity of the field theory up to this 