Orbifolds as Melvin Geometry

TL;DR

This work demonstrates that abelian orbifolds, including $C^2/{\mathbb Z}_N$ ALE spaces, arise as small-radius limits of NSNS Melvin backgrounds with rational magnetic parameters, linking type II and type 0 theories via exact marginal deformations. It extends the construction to higher-dimensional Melvin geometries to realize $C^2/{\mathbb Z}_N$ and related orbifolds as solvable, non-compact vacua with H-flux, and analyzes the resulting mass spectra and tachyon structure. The authors provide explicit partition functions, discuss T-duality relationships, and explore the potential for tachyon condensation and decay pathways, as well as connections to M-theory through the 9-11 flip and F5-brane configurations. Overall, the paper offers a unified, calculable framework connecting SUSY and non-SUSY orbifolds as moduli-space deformations of flat string theory and outlines future directions for non-abelian orbifolds and brane realizations.

Abstract

In this paper we explicitly show that the various noncompact abelian orbifolds are realized as special limits of parameters in type II (NSNS) Melvin background and its higher dimensional generalizations. As a result the supersymmetric ALE spaces (A-type C^2/Z_N) and nonsupersymmetric orbifolds in type II and type 0 theory are all connected with each other by the exactly marginal deformation. Our results provide new examples of the duality between type II and type 0 string theory. We also discuss the decay of unstable backgrounds in this model which include closed string tachyons.

Figures (2)

• Figure 1: Moduli space of the string models in type IIA Melvin backgrounds with $\beta=0$.
• Figure 2: Moduli space of the string models in the higher dimensional Melvin background.