Induced scalar potentials for hypermultiplets

TL;DR

This paper calculates the effective scalar potentials for hypermultiplets in N=2 supersymmetric gauge theories, revealing how non-trivial self-interactions and scalar potentials arise in Coulomb and Higgs branches, linked to specific hyper-Kähler metrics.

Contribution

It provides explicit calculations of scalar potentials for hypermultiplets, connecting these to the Taub-NUT and Eguchi-Hanson hyper-Kähler metrics in the low-energy effective action.

Findings

Scalar potential for charged hypermultiplet in Coulomb branch derived.

Scalar potential for neutral hypermultiplet in Higgs branch derived.

Connections established between potentials and specific hyper-Kähler metrics.

Abstract

Charged BPS hypermultiplets can develop a non-trivial self-interaction in the Coulomb branch of an N=2 supersymmetric gauge theory, whereas neutral BPS hypermultiplets in the Higgs branch may also have a non-trivial self-interaction in the presence of Fayet-Iliopoulos terms. The exact hypermultiplet low-energy effective action (LEEA) takes the form of the non-linear sigma-model (NLSM) with a hyper-K"ahler metric. A non-trivial scalar potential is also quantum-mechanically generated at non-vanishing central charges, either perturbatively (Coulomb branch), or non-perturbatively (Higgs branch). We calculate the effective scalar potentials for (i) a single charged hypermultiplet in the Coulomb branch and (ii) a single neutral hypermultiplet in the Higgs branch. The first case corresponds to the NLSM with the Taub-NUT (or KK-monopole) metric for the kinetic LEEA, whereas the second one is attached to the NLSM having the Eguchi-Hanson instanton metric.