Induced hypermultiplet self-interactions in N=2 gauge theories

TL;DR

This paper computes the low-energy effective action for hypermultiplets in 4D, N=2 gauge theories using harmonic superspace, revealing induced hyper-Kähler metrics, scalar potentials, and the effects of central charges and FI terms.

Contribution

It introduces a harmonic superspace approach to derive hypermultiplet self-interactions, connecting central charges with internal symmetries and exploring effects of FI terms.

Findings

Induced hyper-Kähler metrics include Taub-NUT and Eguchi-Hanson types.

The harmonic superspace method shows equivalence of two approaches to central charges.

Fayet-Iliopoulos terms do not destabilize perturbative Taub-NUT self-couplings.

Abstract

We calculate the charged hypermultiplet low-energy effective action in the Coulomb branch of the 4D, N=2 gauge theory, by using the harmonic superspace approach. We find that the unique leading contribution is given by the harmonic-analytic Lagrangian of the fourth order in the hypermultiplet superfields, with the induced coupling constant being proportional to central charges of N=2 SUSY algebra. The central charges are identified with Cartan generators of the internal symmetry, and they give BPS masses to the hypermultiplets. The induced hyper-K"ahler metrics appear to be the Taub-NUT metric or its higher-dimensional generalizations. Simultaneously, non-trivial scalar potentials are produced. Within the harmonic superspace method, we show an equivalence between the two known approaches to the 4D central charges. In the first one, the central charges are obtained via the Scherk-Schwarz dimensional reduction from six dimensions, whereas in the second one they are generated by a covariantly-constant background gauge superfield. Our analysis is extended to a more general situation with the non-vanishing Fayet-Iliopoulos (FI) terms. The perturbatively-induced Taub-NUT self-coupling in the Coulomb branch is found to be stable against adding the FI term, whereas the non-perturbatively generated (Eguchi-Hanson type) hypermultiplet self-interaction is proposed for the Higgs branch.