Local Grand Unification in the Heterotic Landscape

TL;DR

This paper explores how string theory can lead to grand unification at energies below the string scale, using a six-dimensional effective theory derived from heterotic string compactification, with anomaly cancellation and symmetry considerations.

Contribution

It introduces a method to relate effective theory couplings to vacuum location, develops an algorithm for superpotential calculation, and links bulk fields to moduli in orbifold compactifications.

Findings

Anomaly cancellation in the model despite local anomalous U(1) symmetries

Development of an algorithm for superpotential computation to arbitrary order

Establishment of a correspondence between bulk fields and moduli in orbifold models

Abstract

We consider the possibility that the unification of the electroweak interactions and the strong force arises from string theory, at energies significantly lower than the string scale. As a tool, an effective grand unified field theory in six dimensions is derived from an anisotropic orbifold compactification of the heterotic string. It is explicitly shown that all anomalies cancel in the model, though anomalous Abelian gauge symmetries are present locally at the boundary singularities. In the supersymmetric vacuum additional interactions arise from higher-dimensional operators. We develop methods that relate the couplings of the effective theory to the location of the vacuum, and find that unbroken discrete symmetries play an important role for the phenomenology of orbifold models. An efficient algorithm for the calculation of the superpotential to arbitrary order is developed, based on symmetry arguments. We furthermore present a correspondence between bulk fields of the orbifold model in six dimensions, and the moduli fields that arise from compactifying four internal dimensions on a manifold with non-trivial gauge background.