Line bundles in supersymmetric coset models

TL;DR

This paper explores the relationship between line bundles, anomaly cancellation, and Kaehler potentials in supersymmetric sigma-models on coset spaces, highlighting topological constraints and their implications for model consistency.

Contribution

It determines Kaehler potentials for minimal singlet chiral superfields on any compact Kaehlerian coset space and analyzes the quantization conditions affecting anomaly cancellation.

Findings

Quantization conditions can conflict with anomaly cancellation requirements.

Explicit analysis of E_6/SO(10)xU(1) and SU(5)/SU(2)xU(1)xSU(3) models.

Line bundle structures influence model consistency and anomaly freedom.

Abstract

The scalars of an N = 1 supersymmetric sigma-model in 4 dimensions parameterize a Kaehler manifold. The transformations of their fermionic superpartners under the isometries are often anomalous. These anomalies can be canceled by introducing additional chiral multiplets with appropriate charges. To obtain the right charges a non-trivial singlet compensating multiplet can be used. However when the topology of the underlying Kaehler manifold is non-trivial, the consistency of this multiplet requires that its charge is quantized. This singlet can be interpreted as a section of a line bundle. We determine the Kaehler potentials corresponding to the minimal non-trivial singlet chiral superfields for any compact Kaehlerian coset space G/H. The quantization condition may be in conflict with the requirement of anomaly cancelation. To illustrate this, we discuss the consistency of anomaly free models based on the coset spaces E_6/SO(10)xU(1) and SU(5)/SU(2)xU(1)xSU(3).