EXACT LOW-ENERGY EFFECTIVE ACTIONS FOR HYPERMULTIPLETS IN FOUR DIMENSIONS

Abstract

We consider the general hypermultiplet low-energy effective action (LEEA) that may appear in quantized, four-dimensional, N=2 supersymmetric, gauge theories, e.g. in the Coulomb and Higgs branches. Our main purpose is a description of the exact LEEA of n magnetically charged hypermultiplets. The hypermultiplet LEEA is given by the N=2 supersymmetric nonlinear sigma-model (NLSM) with a 4n-dimensional hyper-Kähler metric, subject to nonanomalous symmetries. Harmonic superspace (HSS) and the NLSM isometries are very useful to constrain the hyper-Kähler geometry of the LEEA. We use N=2 supersymmetric projections of HSS superfields to N=2 linear (tensor) O(2) and O(4) multiplets in N=2projective superspace (PSS) to deduce the explicit form of the LEEA in some particular cases. As the by-product, a simple new classification of all multimonopole moduli space metrics having su (2)R symmetry is proposed in terms of real quartic polynomials of 2n variables, modulo Sp (n) transformations. The 4d hypermultiplet LEEA for n=2 can be encoded in terms of an elliptic curve.