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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 ℤ2 automorphism swapping the two E8 factors in the supersymmetric heterotic string is also non-anomalous.
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 ℤ2 automorphism swapping the two E8 factors in the supersymmetric heterotic string is also non-anomalous.
The Fayet–Iliopoulos D-term is a common feature in $${\mathcal {N}}=1$$ N = 1 string vacua that contain an anomalous U(1) gauge symmetry, and arises from a one-loop diagram in string perturbation theory. The same diagram is generated in string vacua in which supersymmetry is broken directly at the string scale, either via spontaneous Scherk–Schwarz breaking, in which case the gravitino mass is determined by the radius of the circle used in the Scherk–Schwarz mechanism, or via explicit supersymmetry breaking by the GSO projections. We analyse the resulting would-be Fayet–Illiopoulos D-term in the non-supersymmetric string vacua and its contribution to the vacuum energy. A numerical estimate in an explicit tachyon-free string-derived model suggests that the would-be D-term contribution may uplift the vacuum energy to a positive value.
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