New string theory vacua with suppressed proton decay.

摘要

In this thesis we construct new heterotic superstring vacua with suppressed proton decay. More concretely, we construct Calabi-Yau threefolds Z with fundamental group $Z2\times Z2$. These threefolds carry Ricci flat hermitian metrics [48] which we use to solve the gravitational part of the string theory equation of motions. Furthermore, these Calabi-Yau threefolds allow the existence of $Z2\times Z2$ Wilson loops.; On these threefolds Z we construct stable, holomorphic vector bundles with SU(4) structure group. It follows from a famous theorem by Donaldson [20], Uhlenbeck and Yau [47] that these vector bundles correspond to gauge field configurations whose fields strength obey the hermitian Yang-Mills equations. Therefore, in constructing these vector bundles, we solve the gauge theoretic part of the string theory equations of motion.; These vacuum solutions of heterotic string theory give, in conjunction with $Z2\times Z2$ Wilson loops, consistent four dimensional N = 1 supersymmetric vacua with three families of quarks and leptons. The four dimensional gauge group is the standard-model-like group SU3C× SU2W×U 1Y×U1 B-L. The additional gauge symmetry U(1) _B–L is used to suppress the most egregious proton decay modes.; In addition, we calculate in this thesis the moduli space of SU(n) × SU( m) vector bundles on simply connected Calabi-Yau spaces X. Such gauge configurations can arise in strongly coupled heterotic string theory in certain phase transitions [42], called small instanton transitions [52].