CNM models, holomorphic functions and projective superspace c-maps

Abstract

Continuing the investigation of CNM (chiral-non-minimal) hypermultiplet non-linear σ-models, we propose extensions of the concept of the c-map which relate holomorphic functions to hyper-Kähler geometrics. In particular, we show that a whole series of hyper-Kähler potentials can be derived by replacing the role of the 4D, N = 1 tensor multiplet in the original c-map by 4D, N = 1 non-minimal multiplets and auxiliary superfields. The resulting N = 2 models appear to have interesting connections to Calabi-Yau manifolds and algebraic varieties. These models also emphasize the fact that special hyper-Kähler manifolds (the analogs of special Kähler manifolds) without isometries exist.