CNM Models, Holomorphic Functions and Projective Superspace C-Maps

TL;DR

This paper extends the c-map concept to relate holomorphic functions with hyper-Kahler geometries using CNM hypermultiplet models, revealing new structures and connections to Calabi-Yau manifolds.

Contribution

It introduces a novel extension of the c-map involving non-minimal multiplets, leading to new hyper-Kahler potentials and models with unique geometric properties.

Findings

Derived new hyper-Kahler potentials using non-minimal multiplets.

Established connections between hyper-Kahler models and Calabi-Yau manifolds.

Showed existence of special hyper-Kahler manifolds without isometries.

Abstract

Continuing the investigation of CNM (chiral-nonminimal) hypermultiplet nonlinear sigma-models, we propose extensions of the concept of the c-map which relate holomorphic functions to hyper-Kahler geometries. In particular, we show that a whole series of hyper-Kahler 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-Kahler manifolds (the analogs of special Kahler manifolds) without isometries exist.