Anomaly Cancellation in Six Dimensions

TL;DR

This paper demonstrates that anomaly cancellation conditions uniquely determine key topological numbers in six-dimensional Calabi-Yau compactifications, and explores their implications for model building and orbifold constructions.

Contribution

It explicitly constructs Green-Schwarz counterterms, derives charge sum rules, and compares these with Abelian orbifold models, including asymmetric cases, providing a geometric interpretation.

Findings

Anomaly cancellation conditions determine topological numbers in 6D compactifications.

Green-Schwarz counterterms are explicitly constructed for these models.

Comparison with orbifold constructions confirms geometric interpretations.

Abstract

I show that anomaly cancellation conditions are sufficient to determine the two most important topological numbers relevant for Calabi-Yau compactification to six dimensions. This reflects the fact that K3 is the only non-trivial CY manifold in two complex dimensions. I explicitly construct the Green-Schwarz counterterms and derive sum rules for charges of additional enhanced U(1) factors and compare the results with all possible Abelian orbifold constructions of K3. This includes asymmetric orbifolds as well, showing that it is possible to regain a geometrical interpretation for this class of models. Finally, I discuss some models with a broken $E_7$ gauge group which will be useful for more phenomenological applications.