# Discrete remnants of orbifolding

## TL;DR

This paper investigates residual symmetries in orbifold projections, revealing previously overlooked transformations, including outer automorphisms, with examples like left-right parity in the Pati-Salam model.

## Contribution

It identifies new residual symmetries in orbifolding, expanding understanding of symmetry transformations, including outer automorphisms, in specific models.

## Key findings

- Discovery of additional residual symmetries in orbifold projections
- Identification of outer automorphisms as residual symmetries
- Application to left-right parity in Pati-Salam model

## Abstract

We revisit the residual symmetries that survive the orbifold projections, and find additional transformations that have been overlooked in the past. Some of these transformations are outer automorphisms of the downstairs continuous symmetry group. Examples for these transformations include the left-right parity of the Pati-Salam model and its left-right symmetric subgroup.