Hidden Sectors from Multiple Line Bundles for the $B-L$ MSSM

TL;DR

This paper develops a formalism for constructing hidden sector bundles in heterotic M-theory using multiple line bundles, applied to a specific threefold model relevant for realistic particle physics, and explores the space of solutions.

Contribution

It introduces a method to build hidden sector bundles as extensions of line bundles, expanding the variety of possible solutions in heterotic M-theory models.

Findings

Constructed explicit examples of hidden sector bundles with multiple line bundles.

Identified six inequivalent extension branches, broadening the solution space.

Ensured the bundles satisfy stability and supersymmetry conditions.

Abstract

We give a formalism for constructing hidden sector bundles as extensions of sums of line bundles in heterotic $M$-theory. Although this construction is generic, we present it within the context of the specific Schoen threefold that leads to the physically realistic $B-L$ MSSM model. We discuss the embedding of the line bundles, the existence of the extension bundle, and a number of necessary conditions for the resulting bundle to be slope-stable and thus $N=1$ supersymmetric. An explicit example is presented, where two line bundles are embedded into the $SU(3)$ factor of the $E_{6} \times SU(3)$ maximal subgroup of the hidden sector $E_{8}$ gauge group, and then enhanced to a non-Abelian $SU(3)$ bundle by extension. For this example, there are in fact six inequivalent extension branches, significantly generalizing that space of solutions compared with hidden sectors constructed from a single line bundle.