Bordism for the 2-group symmetries of the heterotic and CHL strings

TL;DR

This paper investigates the 2-group symmetries of heterotic and CHL strings with nonzero B-fields by computing related bordism groups, which are then used to analyze anomalies and defects in these theories.

Contribution

It expresses the relevant bordism groups as twisted string bordism groups and computes them up to dimension 11, advancing understanding of symmetries and anomalies in these string theories.

Findings

Computed twisted string bordism groups up to dimension 11.

Identified anomalies and defects related to 2-group symmetries.

Provided a framework for analyzing string symmetries using bordism theory.

Abstract

In the presence of a nonzero B-field, the symmetries of the $\mathrm E_8\times \mathrm E_8$ heterotic string form a 2-group, or a categorified group, as do the symmetries of the CHL string. We express the bordism groups of the corresponding tangential structures as twisted string bordism groups, then compute them through dimension 11 modulo a few unresolved ambiguities. Then, we use these bordism groups to study anomalies and defects for these two string theories.