Heterotic Strings and Quantum Entanglement

TL;DR

This paper develops heterotic string orbifolds suitable for calculating quantum entanglement entropy, revealing how gauge symmetry breaking via Wilson lines affects modular invariance and tachyonic contributions.

Contribution

It introduces a novel heterotic string construction for entanglement entropy calculations, classifies symmetry breaking patterns, and analytically continues tachyonic contributions.

Findings

Successfully constructed $ ext{Z}_N$ orbifolds for heterotic strings

Classified all gauge symmetry breaking patterns

Achieved finite analytic continuation of tachyonic contributions

Abstract

We construct $\mathbb{Z}_N$ orbifolds of the ten-dimensional heterotic string theories appropriate for implementing the stringy replica method for the calculation of quantum entanglement entropy. A novel feature for the heterotic string is that the gauge symmetry must be broken by a Wilson line to ensure modular invariance. We completely classify the patterns of symmetry breaking. We show that the tachyonic contributions in all cases can be analytically continued, with a finite answer in the domain $0<N \leq 1$, relevant for calculating entanglement entropy across the Rindler horizon. We discuss the physical implications of our results.