Rigid N=2 superconformal hypermultiplets
Bernard de Wit, Bas Kleijn, Stefan Vandoren
TL;DR
The paper develops a framework for rigid $N=2$ superconformal hypermultiplets coupled to gauge fields associated with hyper-Kähler target-space isometries. It derives the geometric data and transformation rules of hypermultiplets, analyzes the gauging of isometries producing moment maps, and constructs the corresponding scalar potential and Yukawa couplings, ensuring supersymmetry. It further imposes rigid superconformal invariance to obtain constraints such as a homothetic Killing vector and relations tying the SU(2) and U(1) R-symmetries to the hyper-Kähler structure, showing how vector-multiplet actions compatible with conformal symmetry arise from homogeneous holomorphic data. The results clarify how hypermultiplet sectors can be coupled to conformal supergravity in parallel with vector-multiplet special geometry and lay out the precise geometric conditions for superconformal invariance.
Abstract
We discuss superconformally invariant systems of hypermultiplets coupled to gauge fields associated with target-space isometries.