Mirage Torsion

TL;DR

This paper demonstrates that discrete torsion in Z_NxZ_M orbifold models can be transformed into equivalent torsionless models by lattice shifts, offering a new perspective on their classification and background field configurations.

Contribution

It shows how discrete torsion phases can be gauged away or traded for background field changes, and introduces a classification method for heterotic Z_NxZ_M orbifolds.

Findings

Discrete torsion can be 'gauged away' via lattice shifts.

Generalized discrete torsion phases can be replaced by background field modifications.

A new classification method for heterotic Z_NxZ_M orbifolds is proposed.

Abstract

Z_NxZ_M orbifold models admit the introduction of a discrete torsion phase. We find that models with discrete torsion have an alternative description in terms of torsionless models. More specifically, discrete torsion can be 'gauged away' by changing the shifts by lattice vectors. Similarly, a large class of the so-called generalized discrete torsion phases can be traded for changing the background fields (Wilson lines) by lattice vectors. We further observe that certain models with generalized discrete torsion are equivalent to torsionless models with the same gauge embedding but based on different compactification lattices. We also present a method of classifying heterotic Z_NxZ_M orbifolds.