Matter coupling and anomaly cancellation in supersymmetric sigma-models

TL;DR

This paper develops a generalized framework for matter couplings in 4D supersymmetric sigma models on Kaehler manifolds, enabling anomaly cancellation and consistent gauging of symmetries, with applications to specific coset spaces.

Contribution

It introduces a method to assign arbitrary U(1) charges to matter fermions in supersymmetric sigma models, allowing anomaly cancellation and consistent gauging of isometries.

Findings

Allows elimination of gamma_5 anomalies in U(1) symmetries.

Enables spontaneous symmetry breaking via supersymmetric Higgs mechanism.

Provides explicit example with E6/SO(10) x U(1) coset space.

Abstract

Generalized matter couplings to four-dimensional supersymmetric sigma models on general Kaehler manifolds are presented, preserving all holomorphic symmetries. Our generalization allows assignment of arbitrary U(1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted gamma_5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of a chiral scalar multiplet, the U(1) symmetry is broken spontaneously, generating a mass for the U(1) vector multiplet via the supersymmetric Higgs effect. As an example we discuss the case of the homogeneous coset space E6/SO(10) x U(1).