Anisotropic Solutions For Orbifold Moduli From Duality Invariant Gaugino Condensates

TL;DR

This paper investigates the behavior of certain orbifold moduli in string theory, focusing on their transformation properties and stabilization via duality-invariant gaugino condensates, especially in complex fixed-plane scenarios.

Contribution

It provides new solutions for orbifold moduli that account for anisotropic conditions and fixed planes, extending previous models to more general orbifold geometries.

Findings

Derived moduli values from a duality invariant potential.

Identified conditions where moduli transform under subgroups of SL(2,Z).

Presented anisotropic solutions for orbifold moduli stabilization.

Abstract

The values of the $T$ and $U$ moduli are studied for those ${\bf Z}_N $ Coxeter orbifolds with the property that some of the twisted sectors have fixed planes for which the six-torus ${\bf T}^6 $ can not be decomposed into a direct sum ${\bf T}^2\bigoplus {\bf T}^4 $ with the fixed plane lying in ${\bf T}^2 $. Such moduli in general transform under a subgroup of the modular group $SL(2,Z).$ The moduli are determined by minimizing the effective potential derived from a duality invariant gaugino condensate.