c--Map,very Special Quaternionic Geometry and Dual Ka\"hler Spaces

TL;DR

This paper introduces a dual Kähler geometry for very special quaternionic manifolds, revealing new structures with applications in Type IIB Calabi-Yau orientifold compactifications.

Contribution

It demonstrates a novel N=1 reduction that defines a dual Kähler geometry, expanding the understanding of quaternionic and special Kähler geometries.

Findings

Dual Kähler metric is derived from very special quaternionic manifolds.

The dual geometry has a flat potential similar to the original.

Applications in string compactifications are discussed.

Abstract

We show that for all very special quaternionic manifolds a different N=1 reduction exists, defining a Kaehler Geometry which is ``dual'' to the original very special Kaehler geometry with metric G_{a\bar{b}}= - \partial_a \partial_b \ln V (V={1/6}d_{abc}\lambda^a \lambda^b \lambda^c). The dual metric g^{ab}=V^{-2} (G^{-1})^{ab} is Kaehler and it also defines a flat potential as the original metric. Such geometries and some of their extensions find applications in Type IIB compactifications on Calabi--Yau orientifolds.