Notes on Heterotic Compactifications

TL;DR

This paper clarifies the conditions for anomaly cancellation in heterotic compactifications involving torsion-free sheaves and corrects previous errors in counting massless particles, advancing the understanding of heterotic string theory.

Contribution

It provides a corrected anomaly-freedom condition for heterotic compactifications with torsion-free sheaves and rectifies prior inaccuracies in massless particle counting.

Findings

An example showing the anomaly-freedom condition is incorrect with torsion-free sheaves

Corrections to the literature on counting massless particles in heterotic compactifications

Enhanced understanding of heterotic compactification constraints

Abstract

In this technical note we describe a pair of results on heterotic compactifications. First, we give an example demonstrating that the usual statement of the anomaly-freedom constraint for perturbative heterotic compactifications (meaning, matching second Chern characters) is incorrect for compactifications involving torsion-free sheaves. Secondly, we correct errors in the literature regarding the counting of massless particles in heterotic compactifications.