# Hairs of discrete symmetries and gravity

## TL;DR

The paper argues that discrete symmetries, like gauge symmetries, are respected by gravity due to the existence of string-like configurations (hair) at domain wall intersections, extending the understanding of symmetry conservation.

## Contribution

It introduces the concept of discrete symmetry hair in gravitational contexts, showing that discrete charges are conserved by gravity through domain wall intersections.

## Key findings

- Discrete charges are conserved by gravity.
- String-like configurations (hair) exist at domain wall intersections.
- Discrete symmetries are respected by gravity similar to gauge symmetries.

## Abstract

Gauge symmetries are known to be respected by gravity because gauge charges carry flux lines, but global charges do not carry flux lines and are not conserved by gravitational interaction. For discrete symmetries, they are spontaneously broken in the Universe, forming domain walls. Since the realization of discrete symmetries in the Universe must involve the vacuum expectation values of Higgs fields, a string-like configuration (hair) at the intersection of domain walls in the Higgs vacua can be realized. Therefore, we argue that discrete charges are also respected by gravity.