A fresh view on string orbifolds

TL;DR

This paper introduces a new perspective on string orbifolds by framing them in terms of gauge symmetry groups, highlighting the importance of higher group structures and duality frame dependence.

Contribution

It proposes a novel formulation of string orbifolds based on gauge symmetries, emphasizing the role of higher group structures and providing new insights into their construction.

Findings

Higher group structures influence orbifold gauge groups

Orbifold procedures depend on duality frames

Examples illustrate the role of gauge symmetry breaking

Abstract

In quantum field theory, an orbifold is a way to obtain a new theory from an old one by gauging a finite global symmetry. This definition of orbifold does not make sense for quantum gravity theories, that admit (conjecturally) no global symmetries. In string theory, the orbifold procedure involves the gauging of a global symmetry on the world-sheet theory describing the fundamental string. Alternatively, it is a way to obtain a new string background from an old one by quotienting some isometry. We propose a new formulation of string orbifolds in terms of the group of gauge symmetries of a given string model. In such a formulation, the `parent' and the `child' theories correspond to different ways of breaking or gauging all potential global symmetries of their common subsector. Through a couple of simple examples, we describe how the higher group structure of the gauge group in the parent theory plays a crucial role in determining the gauge group and the twisted sector of the orbifold theory. We also discuss the dependence of this orbifold procedure on the duality frame.