Anomalies, D-flatness and Small Instantons

TL;DR

This paper investigates the effects of shrinking multiple instantons to zero size in six-dimensional heterotic string theory, revealing a subtlety in the moduli space related to anomaly cancellation and D-flatness.

Contribution

It uncovers a subtlety in the moduli space of instantons when many are shrunk to zero size, extending Witten's symmetry enhancement mechanism.

Findings

Identifies a subtlety in the moduli space during instanton shrinking

Demonstrates constraints from anomaly cancellation and D-flatness

Highlights implications for symmetry enhancement in string theory

Abstract

Recently, Witten has proposed a mechanism for symmetry enhancement in $SO(32)$ heterotic string theory, where the singularity obtained by shrinking an instanton to zero size is resolved by the appearance of an $Sp(1)$ gauge symmetry. In this short letter, we consider spacetime constraints from anomaly cancellation in six dimensions and D-flatness and demonstrate a subtlety which arises in the moduli space when many instantons are shrunk to zero size.