Supersymmetric (non-)Abelian Bundles in the Type I and SO(32) Heterotic String

TL;DR

This paper explores the compactification of SO(32) heterotic and Type I strings on Calabi-Yau manifolds with non-abelian and abelian bundles, analyzing anomaly cancellation, threshold corrections, and stability conditions, with implications for phenomenology.

Contribution

It provides a detailed analysis of anomaly cancellation, threshold corrections, and stability conditions for non-abelian bundles in heterotic and Type I string compactifications, including phenomenological considerations.

Findings

Derived non-universal one-loop threshold corrections to gauge kinetic functions.

Analyzed the generalized Green-Schwarz mechanism for multiple anomalous U(1)s.

Discussed the possibility of TeV-scale large extra dimensions in heterotic string scenarios.

Abstract

We discuss perturbative four-dimensional compactifications of both the SO(32) heterotic and the Type I string on smooth Calabi-Yau manifolds endowed with general non-abelian and abelian bundles. We analyse the generalized Green-Schwarz mechanism for multiple anomalous U(1) factors and derive the generically non-universal one-loop threshold corrections to the gauge kinetic function as well as the one-loop corrected Fayet-Iliopoulos terms. The latter can be interpreted as a stringy one-loop correction to the Donaldson-Uhlenbeck-Yau condition. Applying S-duality, for the Type I string we obtain the perturbative Pi-stability condition for non-abelian bundles on curved spaces. Some simple examples are given, and we qualitatively discuss some generic phenomenological aspects of this kind of string vacua. In particular, we point out that in principle an intermediate string scale scenario with TeV scale large extra dimensions might be possible for the heterotic string.