# Transitions of Orbifold Vacua

## TL;DR

This paper explores the structure of heterotic string vacua on orbifolds, revealing how phase transitions involving instantons and 5-branes connect different gauge vacua and affect the spectrum and modular invariance.

## Contribution

It provides a stringy top-down description of gauge symmetry breaking, vacuum transitions, and the interconnectedness of various vacua via instanton and 5-brane dynamics.

## Key findings

- Vacua are connected through instanton and 5-brane transitions.
- Phase transitions explain spectrum and modular invariance conditions.
- Multiple gauge vacua are inherited from perturbative vacua.

## Abstract

We study the global structure of vacua of heterotic strings compactified on orbifolds $T^4/Z_N$ (N=2,3) in the presence of heterotic 5-branes. Gauge symmetry breaking associated with orbifold is described by instantons in the field theory. Phase transition between small instantons and heterotic 5-branes provides top-down, stringy account to the spectrum and modular invariance condition. Also it takes us from one vacuum to another by emitting and absorbing instantons. This means that many vacua with different gauge theory are in fact connected and are inherited from perturbative vacua. It follows that there are also transitions among twisted fields, heterotic 5-branes and instantons.