Kaehler manifolds and supersymmetry

TL;DR

This paper reviews how Kaehler geometry underpins supersymmetric field theories, enabling the construction of anomaly-free models on coset manifolds that serve as alternatives to traditional MSSM and GUT frameworks.

Contribution

It introduces a geometric approach to building anomaly-free supersymmetric models using line-bundle representations on Kaehler coset manifolds.

Findings

Anomalies can be eliminated via line-bundle representations.

Anomaly-free models can be consistently gauged.

Constructs alternatives to MSSM and GUTs.

Abstract

Supersymmetric field theories of scalars and fermions in 4-D space-time can be cast in the formalism of Kaehler geometry. In these lectures I review Kaehler geometry and its application to the construction and analysis of supersymmetric models on Kaehler coset manifolds. It is shown that anomalies can be eliminated by the introduction of line-bundle representations of the coset symmetry groups. Such anomaly-free models can be gauged consistently and used to construct alternatives to the usual MSSM and supersymmetric GUTs.