Duality and Orbifolds

TL;DR

This paper addresses whether orbifolding commutes with duality in string theory and develops a constructive framework to test this by starting from known dual pairs and modding them by paired $Z_2$ symmetries. It presents several explicit dual pairs where the orbifold action is nonfree and analyzes twisted-sector spectra, including the necessity of background strings to cancel one-loop tadpoles. A key finding is that, in many cases, spectrum matching depends on nontrivial identities among tadpole coefficients across heterotic, type II and type I theories, providing stringent consistency checks for duality. The work also clarifies when the adiabatic argument applies and situates these results within a broader classification of orbifold-duality compatibility, with implications for M-theory orbifolds.

Abstract

We construct several examples where duality transformation commutes with the orbifolding procedure even when the orbifolding group does not act freely, and there are massless states from the twisted sector at a generic point in the moduli space. Often the matching of spectrum in the dual theories is a result of non-trivial identities satisfied by the coefficients of one loop tadpoles in the heterotic, type II and type I string theories.