Heterotic GUT and Standard Model Vacua from simply connected Calabi-Yau Manifolds

TL;DR

This work demonstrates that realistic GUT and Standard Model vacua can be engineered in the $E_8\times E_8$ heterotic string on simply connected Calabi–Yau manifolds by using $U(N)$ bundles with nontrivial line factors and including heterotic five-branes. It develops a consistent Green–Schwarz mechanism incorporating M5-branes, derives the one-loop corrected Donaldson–Uhlenbeck–Yau equations, and analyzes gauge couplings and FI terms, showing how five-brane moduli influence threshold corrections. The authors realize flipped $SU(5)\times U(1)_X$ and direct MSSM-like models by embedding line bundles into both $E_8$ factors, thereby keeping a massless $U(1)_X$ or hypercharge without requiring Wilson lines; they provide explicit three-generation examples on elliptically fibered Calabi–Yau manifolds using spectral covers. The results highlight the rich landscape of heterotic vacua on simply connected backgrounds and the pivotal role of abelian bundle data in achieving realistic gauge groups and couplings via threshold corrections within the Horava–Witten regime.

Abstract

We consider four-dimensional supersymmetric compactifications of the E8 x E8 heterotic string on Calabi-Yau manifolds endowed with vector bundles with structure group SU(N) x U(1) and five-branes. After evaluating the Green-Schwarz mechanism and deriving the generalized Donaldson-Uhlenbeck-Yau condition including the five-brane moduli, we show that this construction can give rise to GUT models containing U(1) factors like flipped SU(5) or directly the Standard Model even on simply connected Calabi-Yau manifolds. Concrete realizations of three-generation models on elliptically fibered Calabi-Yau manifolds are presented. They exhibit the most attractive features of flipped SU(5) models such as doublet-triplet splitting and proton stability. In contrast to conventional GUT string models, the tree level relations among the Standard Model gauge couplings at the GUT scale are changed.

Figures (2)

• Figure 1: Green-Schwarz counter term for the mixed gauge anomaly.
• Figure 2: M5-brane potential in Horava-Witten theory on the Quintic induced by abelian gauge flux on $E_8^{(1)}$.