Breakdown of Duality in (0,2) Superstring Models

TL;DR

This paper investigates the modular symmetry groups in (0,2) superstring orbifold models, highlighting how Wilson lines influence these symmetries and providing explicit examples with the $Z_7$ orbifold.

Contribution

It identifies the modular groups for specific orbifolds and demonstrates how quantized Wilson lines can break traditional modular symmetries, offering new insights into superstring compactifications.

Findings

The modular group for the $Z_7$ orbifold differs from $[SL(2,{f Z})]^3$.

Quantized Wilson lines can break $SL(2,{f Z})$ symmetry.

Wilson lines have a nontrivial impact on the modular symmetry structure.

Abstract

After pointing out the role of the compactification lattice for spectrum calculations in orbifold models, I discuss modular discrete symmetry groups for $Z_N$ or\-bi\-folds. I consider the $Z_7$ orbifold as a nontrivial example of a (2,2) model and give the generators of the modular group for this case, which does not contain $[SL(2,{\bf Z})]^3$ as had been speculated. I also discuss how to treat cases where quantized Wilson lines are present. I consider in detail an example, demonstrating that quantized Wilson lines affect the modular group in a nontrivial manner. In particular, I show that it is possible for a Wilson line to break $SL(2,{\bf Z})$.}