# Orbifolds and Orientifolds as O-folds

## TL;DR

This paper introduces O-folds, a generalization of orbifolds and orientifolds, as quotients of string and M-theory by discrete U-duality subgroups, encompassing non-geometric identifications and unifying various duality descriptions.

## Contribution

It presents the concept of O-folds as a new framework for understanding duality quotients, including their analysis via exceptional field theory and fixed point vector multiplets.

## Key findings

- O-folds unify orbifolds and orientifolds within U-duality quotients.
- The framework captures non-geometric identifications in string/M-theory.
- Extra vector multiplets are introduced at fixed points in exceptional field theory.

## Abstract

We consider quotients of string and M-theory by discrete subgroups of the U-duality group. This results in what we call O-folds, which are generalisations of orbifolds and orientifolds, and generically involve non-geometric identifications between physical coordinates and dual winding coordinates. A simple $\mathbb{Z}_2$ quotient encodes the half-maximal duality web, describing on the same footing the Ho\v{r}ava-Witten description of M-theory on an interval, the heterotic theories, and type II in the presence of orientifold planes. This can be analysed using exceptional field theory, including the introduction of extra vector multiplets at the fixed points. This is an overview of the paper [1], based on a talk given at the Corfu Summer Institute 2018.