Homogeneous Special Manifolds, Orientifolds and Solvable Coordinates

TL;DR

This paper explores the geometric structures of N=2 special manifolds relevant to string theory compactifications, focusing on orientifolds and solvable coordinates, revealing how involutions and bulk fields influence symmetries.

Contribution

It introduces new geometric insights into N=2 and N=1 string compactifications, especially regarding involutions and symmetry structures of moduli spaces.

Findings

Properly defined involutions enable N=1 Kaehler subspaces within quaternionic manifolds.

Bulk fields modify the shift symmetry of brane coordinates from abelian to nilpotent algebra.

The work provides a geometric framework connecting orientifolds and solvable coordinates.

Abstract

We discuss some geometrical properties of the underlying N=2 geometry which encompasses some low--energy aspects of N=1 orientifolds as well as four dimensional N=2 Lagrangians including bulk and open string moduli.In the former case we illustrate how properly defined involutions allow to define N=1 Kaehler subspaces of special quaternionic manifolds. In the latter case we show that the full shift symmetry of the brane coordinates, which is abelian in the rigid limit, is partially distorted by bulk fields to a nilpotent algebra.