Anomaly-Free Supersymmetric Models in Six Dimensions

TL;DR

This paper reviews anomaly cancellation conditions for six-dimensional N=1 supersymmetric models, illustrating examples including non-perturbative string theory models and proposing new anomaly-free gauge group configurations.

Contribution

It provides a comprehensive review of anomaly cancellation in 6D supersymmetric models and introduces new classes of models with potential non-perturbative string theory realizations.

Findings

Verified anomaly cancellation for specific models including K3 compactification.

Identified new anomaly-free models with gauge groups $SO(2n+8)\times Sp(n)$ and $SU(n)\times SU(n)$.

Highlighted models not realizable via perturbative string theory.

Abstract

The conditions for the cancellation of all gauge, gravitational, and mixed anomalies of $N=1$ supersymmetric models in six dimensions are reviewed and illustrated by a number of examples. Of particular interest are models that cannot be realized perturbatively in string theory. An example of this type, which we verify satisfies the anomaly cancellation conditions, is the K3 compactification of the $SO(32)$ theory with small instantons recently proposed by Witten. When the instantons coincide it has gauge group $SO(32) \times Sp(24)$. Two new classes of models, for which non-perturbative string constructions are not yet known, are also presented. They have gauge groups $SO(2n+8)\times Sp(n)$ and $SU(n)\times SU(n)$, where $n$ is an arbitrary positive integer.