String Moduli Spaces and Parabolic Factorizations

TL;DR

This paper explores how symmetric spaces in string theory can be decomposed via parabolic subgroups to facilitate parametrizations and analyze moduli spaces, with applications to K3 surfaces and Dynkin diagram manipulations.

Contribution

It introduces explicit metric decompositions of symmetric spaces using parabolic subgroups, enabling new parametrizations and insights into moduli spaces in string theory.

Findings

Explicit metric decompositions of symmetric spaces.

Parametrizations of moduli spaces for K3 surfaces.

Dynkin diagram manipulations for symmetric space transitions.

Abstract

The symmetric spaces that appear as moduli spaces in string theory and supergravity can be decomposed with explicit metrics using parabolic subgroups. The resulting isometry between the original moduli space and this decomposition can be used to find parametrizations of the moduli. One application is to determine the volume parameter in conformal field moduli spaces for K3 surfaces. Other applications involve simple Dynkin diagram manipulations inducing "going up and down" between symmetric spaces by adding parameters and going to limits respectively. For supersymmetries such as N=6, this involves combinatorics of less familiar "restricted" Dynkin diagrams.