Metric Building of pp Wave Orbifold Geometries

TL;DR

This paper investigates string theory on orbifolded pp wave backgrounds derived from $AdS_{5} imes S^5$ by SU(2) discrete groups, utilizing singularity theory and conformal field theory to derive explicit metric dependencies.

Contribution

It introduces a method to derive degenerate metrics of orbifolded pp wave geometries using $ADE$ singularities and CFT results, providing explicit moduli dependencies for various orbifolds.

Findings

Derived explicit metrics for orbifolded pp wave geometries.

Connected singularity theory with string backgrounds.

Provided moduli dependence formulas for orbifolds.

Abstract

We study strings on orbifolds of $AdS_{5}\times S^5$ by SU(2) discrete groups in the Penrose limit. We derive the degenerate metrics of pp wave of $AdS_{5}\times S^5/\Gamma$ using ordinary $ADE$ and affine $\wildtilde{ADE}$ singularities of complex surfaces and results on ${\cal N}=4$ CFT$_4$'s. We also give explicit metric moduli depencies for abelian and non abelian orbifolds.