SU(4) Instantons on Calabi-Yau Threefolds with Z_2 x Z_2 Fundamental Group

TL;DR

This paper constructs and analyzes SU(4) instantons on Calabi-Yau threefolds with Z_2 x Z_2 fundamental group, exploring their role in heterotic string compactifications that yield realistic particle physics models.

Contribution

It introduces invariant, stable, holomorphic rank four vector bundles on Calabi-Yau threefolds with Z_2 x Z_2 symmetry, leading to new heterotic vacua compatible with phenomenology.

Findings

Constructed families of SU(4) instantons satisfying particle physics constraints

Presented discrete parameter spaces and moduli bounds for these instantons

Demonstrated potential for realistic low-energy models with U(1)_{B-L} symmetry

Abstract

Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with Z_2 x Z_2 fundamental group are presented. This is accomplished by constructing invariant, stable, holomorphic rank four vector bundles on the simply connected cover of Z. Such bundles can descend either to Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is shown that large families of such instantons satisfy the constraints imposed by particle physics phenomenology. The discrete parameter spaces of those families are presented, as well as a lower bound on the dimension of the continuous moduli of any such vacuum. In conjunction with Z_2 x Z_2 Wilson lines, these SU(4) gauge vacua can lead to standard-like models at low energy with an additional U(1)_{B-L} symmetry. This U(1)_{B-L} symmetry is very helpful in naturally suppressing nucleon decay.