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

Abstract

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 $M_{GUT}\sim 2\times 10^{16}GeV$ as the unification scale with precise gauge coupling unification of $SU(3)\times SU(2)\times U(1{)}_Y$. We choose ${\alpha }_{GUT}^{-1}\sim 24$. 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.

Comments: 5 pages, this revised version corrects some equations in the first version. The bottom line remains unchanged