A perfect match of MSSM-like orbifold and resolution models via anomalies

TL;DR

This paper demonstrates a precise correspondence between orbifold and smooth resolution models in heterotic string compactifications by matching spectra and anomalies, facilitating computations on smooth manifolds.

Contribution

It establishes a perfect mapping of chiral spectra and anomalies between orbifold models and their blow-up resolutions, enhancing the understanding of string compactifications.

Findings

Exact match of chiral spectra between models

Identification of anomaly cancellation mechanisms

Relevance of field redefinitions for interactions

Abstract

Compactification of the heterotic string on toroidal orbifolds is a promising set-up for the construction of realistic unified models of particle physics. The target space dynamics of such models, however, drives them slightly away from the orbifold point in moduli space. This resolves curvature singularities, but makes the string computations very difficult. On these smooth manifolds we have to rely on an effective supergravity approximation in the large volume limit. By comparing an orbifold example with its blow-up version, we try to transfer the computational power of the orbifold to the smooth manifold. Using local properties, we establish a perfect map of the the chiral spectra as well as the (local) anomalies of these models. A key element in this discussion is the Green-Schwarz anomaly polynomial. It allows us to identify those redefinitions of chiral fields and localized axions in the blow-up process which are relevant for the interactions (such as Yukawa-couplings) in the model on the smooth space.