Non-Abelian Brane Worlds: The Heterotic String Story

TL;DR

The authors develop a framework for realistic four-dimensional vacua in the $SO(32)$ heterotic string by employing direct sums of stable unitary bundles and heterotic five-branes on elliptically fibered Calabi–Yau manifolds. They leverage the spectral cover construction and line-bundle twisting to build $U(n)$ bundles, analyze the resulting massless spectra, and enforce SUSY and anomaly-cancellation constraints, including a generalized Green-Schwarz mechanism. By specializing to del Pezzo bases, they construct explicit semi-realistic models: a four-generation Pati-Salam model on $dP_3$ and a three-generation MSSM-like model on $dP_4$, demonstrating viable chiral content and flux/tadpole consistency in perturbative regimes and illustrating the role of H5-branes in tadpole cancellation. The work shows that SO(32) heterotic compactifications can realize MSSM-like physics with explicit bundle data and a clear duality relation to Type I open-string constructions, contributing to the string landscape of realistic vacua.

Abstract

We discuss chiral supersymmetric compactifications of the SO(32) heterotic string on Calabi-Yau manifolds equipped with direct sums of stable bundles with structure group U(n). In addition we allow for non-perturbative heterotic five-branes. These models are S-dual to Type I compactifications with D9- and D5-branes, which by themselves are mirror symmetric to general intersecting D6-brane models. For the construction of concrete examples we consider elliptically fibered Calabi-Yau manifolds with SU(n) bundles given by the spectral cover construction. The U(n) bundles are obtained via twisting by line bundles. We present a four-generation Pati-Salam and a three-generation Standard-like model.