For a full mathematical definition of 'orbifold' summarized above, check A. Adem and M. Klaus. String-theory compactifications on N-dimensional orbifolds is attractive, and essential in some cases. For N = 6, it allows the full determination of the emergent four-dimensional effective supergravity theory, including the gauge group and matter content, the superpotential and Kähler potential, as well as the gauge kinetic function, and yields the four-dimensional space-time supersymmetry-RT.
Before proceeding, what is in an equation like ...
where integration on a global quotient is defined by
and is a G-invariant differential form, where is the inertia stack of , an orbifold groupoid, yeilding the Poincaré pairing on defined as the direct sum of the pairings