Hidden symmetries, special geometry and quaternionic manifolds

TL;DR

This paper explores the symmetry structures of special geometries in string theory moduli spaces, revealing hidden symmetries and their implications for classifying quaternionic spaces.

Contribution

It analyzes the symmetry structures of special real, complex, and quaternionic spaces and their interrelations via dimensional reduction, highlighting hidden symmetries and classification implications.

Findings

Identification of extra and hidden symmetries in special geometries

Application to homogeneous special spaces and quaternionic classification

Insights into symmetry structures of Calabi-Yau moduli spaces

Abstract

The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same {\em special geometry} that is known from nonlinear sigma models in $N=2$ supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of {\em extra} and {\em hidden} symmetries. This analysis is then applied to homogeneous special spaces and the implications for the classification of homogeneous quaternionic spaces are discussed.