Resolution of orbifold singularities for shiftless T7/Z2^3 constructions

Determine an explicit resolution procedure for the orbifold singularities arising in the standard shiftless Z2^3 orbifold of the flat seven-torus T7 used for type IIB compactifications that would feature seven sets of O5-planes (and an O9-plane). Develop a concrete blow-up or smoothing construction that preserves the required orientifold and flux constraints, thereby enabling controlled treatments of these singular geometries within this compactification framework.

Background

In the paper, the author contrasts the use of orbifolds with shifts—which have ‘good’ singularities amenable to Joyce-style blow-ups on the flat T7—with the earlier constructions employing standard Z2^3 orbifolds without shifts that would generate seven sets of O5-planes. The latter require additional D5-branes for tadpole cancellation and also introduce an O9-plane, pushing the setup to type I string theory.

A key obstacle for the shiftless orbifolds is the lack of a known procedure to resolve their orbifold singularities even in the flat T7 case, which prevents establishing well-controlled compactifications within that class. The current paper circumvents this by using shifted orbifolds, but the unresolved issue remains for the shiftless constructions noted in the literature.