Exact hypermultiplet dynamics in four dimensions

Abstract

We use N=2 harmonic and projective superspaces to formulate the most general `Ansatz' for the SU(2)_R invariant hypermultiplet low-energy effective action (LEEA) in four dimensions, which describes the two-parametric family of the hyper-K"ahler metrics generalizing the Atiyah-Hitchin metric. We then demonstrate in the very explicit and manifestly N=2 supersymmetric way that the (magnetically charged, massive) single hypermultiplet LEEA in the underlying non-abelian N=2 supersymmetric quantum field theory can receive both perturbative (e.g., in the Coulomb branch) and non-perturbative (e.g., in the Higgs branch) quantum corrections. The manifestly N=2 supersymmetric Feynman rules in harmonic superspace can be used to calculate the perturbative corrections described by the Taub-NUT metric. The non-perturbative corrections (due to instantons and anti-instantons) can be encoded in terms of an elliptic curve, which is very reminiscent to the Seiberg-Witten theory. Our four-dimensional results agree with the three-dimensional Seiberg-Witten theory and instanton calculations.

14 pages, LaTeX, 1 figure; substantial reduction (by 1/3)

Cited by in corpus (6)

• Universal hypermultiplet metrics
• Superconformal hypermultiplets in superspace
• Gravitational dressing of D-instantons
• One-loop divergences in the six-dimensional $\mathcal{N}=(1,0)$ hypermultiplet self-coupling model
• Exact low-energy effective actions for hypermultiplets in four dimensions
• Anomalous N=2 superconformal Ward identities