Duality and Orbifolds

TL;DR

This paper explores how duality transformations can commute with orbifolding in string theories, even with non-free actions, revealing new spectrum matching mechanisms involving twisted sectors and one-loop tadpole identities.

Contribution

It provides explicit examples demonstrating the compatibility of duality and orbifolding beyond free actions, highlighting the role of non-trivial tadpole coefficient identities.

Findings

Duality commutes with orbifolding in non-free action cases.

Massless twisted sector states appear at generic moduli space points.

Spectrum matching relies on identities of one-loop tadpole coefficients.

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.