Global anomalies & bordism of non-supersymmetric strings

TL;DR

This paper investigates the global consistency of non-supersymmetric string theories in ten dimensions by computing their bordism groups to identify potential anomalies, confirming their absence in most cases and exploring implications for brane classification.

Contribution

It computes twisted string bordism groups for non-supersymmetric strings, revealing the absence of global anomalies in two models and partial results in the third, advancing understanding of their consistency.

Findings

Vanishing of twisted bordism groups in Sugimoto and $SO(16)^2$ models

Partial vanishing in Sagnotti 0'B model

Reproof of non-anomalous $ ext{Z}_2$ automorphism in heterotic string

Abstract

The three tachyon-free non-supersymmetric string theories in ten dimensions provide a handle on quantum gravity away from the supersymmetric lamppost. However, they have not been shown to be fully consistent; although local anomalies cancel due to versions of the Green-Schwarz mechanism, there could be global anomalies, not cancelled by the Green-Schwarz mechanism, that could become fatal pathologies. We compute the twisted string bordism groups that control these anomalies via the Adams spectral sequence, showing that they vanish completely in two out of three cases (Sugimoto and $SO(16)^2$) and showing a partial vanishing also in the third (Sagnotti 0'B model). We also compute lower-dimensional bordism groups of the non-supersymmetric string theories, which are of interest to the classification of branes in these theories via the Cobordism Conjecture. We propose a worldvolume content based on anomaly inflow for the $SO(16)^2$ NS5-brane, and discuss subtleties related to the torsion part of the Bianchi identity. As a byproduct of our techniques and analysis, we also reprove that the outer $\mathbb{Z}_2$ automorphism swapping the two $E_8$ factors in the supersymmetric heterotic string is also non-anomalous.