Relative Scales of the GUT and Twin Sectors in an F-theory model

In this letter we analyze the relative scales for the GUT and twin sectors in the F-theory model discussed in Ref. \cite{Clemens-3}. There are a number of volume moduli in the model. The volume of the GUT surface in the visible sector {[}sector(1){]} (with the Wilson line GUT breaking) defines the GUT scale $M_{GUT}\sim2\times10^{16}~GeV$ as the unification scale with precise gauge coupling unification of $SU(3)\times SU(2)\times U(1)_{Y}$. We choose $\alpha_{GUT}^{-1}\sim24$. We are then free to choose the ratio $\alpha_{G}(2)/\alpha_{G}(1)=m_{1}/m_{2}$ with $m(1)$ and $m(2)$ independent volume moduli associated with the directions perpendicular to the two GUT surfaces. We then analyze the effective field theory of the twin sector(2), which may lead to a SUSY breaking gaugino condensate. Of course, all these results are subject to the self-consistent stabilization of the moduli.