GLSM resolutions of torsional heterotic ℤ2×ℤ2 orbifolds

Heterotic toriodal [Formula: see text] orbifolds may possess discrete torsion between the two defining orbifold twists in the form of additional cocycle factors in their one-loop partition functions. Using Gauged Linear Sigma Models (GLSMs) the consequences of discrete torsion can be uncovered when the orbifold is smoothed out by switching on appropriate blowup modes. Here blowup modes with twisted oscillator excitations are chosen to reproduce bundles that are close to the standard embedding without torsion. The orbifold resolutions with discrete torsion are distinguished from resolutions without torsion, since they require NS5-branes at their exceptional cycles.