Small Yukawa Couplings from Type I String Theory and the Inflationary Solution to the Strong CP and μ Problems

We investigate the origin of phenomenologically interesting small Yukawa couplings in Type I string theory. Utilising the framework of intersecting sets of D9 and orthogonal D5 branes we demonstrate the connection between extra dimensional volumes and Yukawa couplings. For example, we show that extra dimensions with inverse lengths of 10 8 GeV can lead to 10 −10 Yukawa couplings. String selection rules, arising from the D-Brane setup, impose non-trivial constraints on the set of allowed superpotentials. As a phenomenological application of these results we construct a type I string model of inflationary particle physics which involves small Yukawa couplings of order 10 −10 , and simultaneously solves the strong CP and µ problem of the MSSM, via the vacuum expectation value of the inflaton field.