Mirage torsion

Bbb Z_N × Bbb Z_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 Bbb Z_N × Bbb Z_M orbifolds.