Global anomalies & bordism of non-supersymmetric strings

Understand

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.