Higgs Multiplets in Heterotic GUT Models

TL;DR

This paper investigates the calculation of Higgs multiplets in heterotic GUT models, revealing discrepancies in spectral bundle computations that suggest a need for refined geometric analysis.

Contribution

It identifies a mismatch in Higgs number calculations for spectral bundles and proposes that addressing geometric subtleties can resolve this issue.

Findings

Discrepancy found in Higgs count for spectral bundles

Geometric subtleties in spectral data are crucial

Refined analysis can reconcile calculations with expectations

Abstract

For supersymmetric GUT models from heterotic string theory, built from a stable holomorphic SU(n) vector bundle $V$ on a Calabi-Yau threefold $X$, the net amount of chiral matter can be computed by a Chern class computation. Corresponding computations for the number $N_H$ of Higgses lead for the phenomenologically relevant cases of GUT group SU(5) or SO(10) to consideration of the bundle $\La^2 V$. In a class of bundles where everything can be computed explicitly (spectral bundles on elliptic $X$) we find that the computation for $N_H$ gives a result which is in conflict with expectations. We argue that this discrepancy has its origin in the subtle geometry of the spectral data for $\La^2 V$ and that taking this subtlety into account properly should resolve the problem.