Global anomalies & bordism of non-supersymmetric strings

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 ℤ2 automorphism swapping the two E8 factors in the supersymmetric heterotic string is also non-anomalous.

Anomaly constraints for heterotic strings and supergravity in six dimensions

“…Nevertheless, when the 2-form fields of interest are non-chiral, such ambiguities disappear and the anomaly theory turns out to vanish for all the models at stake, including a number of non-supersymmetric heterotic orbifolds. 2 This analysis thus extends the results of [41,42] to some non-supersymmetric settings and those of [38] to lower dimensions.…”

“…Similarly, in section 8 we show that the anomaly cancels for the peculiar "non-geometric" Gepner orientifold with n T = 0 for certain choices of quadratic refinement which however differ from the one defined in [39]. These consistency checks are not a priori trivial, since the analysis of [42] covers heterotic settings (assuming the Stolz-Teichner conjecture [43]) while the analysis of [38] covers smooth geometric compactifications of ten-dimensional models.…”

“…Dai-Freed anomalies [26] comprise both local [27][28][29][30][31] and global [32][33][34][35] anomalies in the traditional sense, but they also include more general anomalies arising from spacetime topology change. Demanding that these anomalies cancel can entail additional, stronger constraints [26,36,37], and their cancellation in (non-)supersymmetric string theories in ten dimensions provides further evidence for their non-perturbative consistency [38].…”

“…In this paper we study Dai-Freed anomalies in 6d N = 1 supergravity, focusing on families of theories with n T = 1 tensor multiplets and simply laced gauge groups. We will also discuss U(1) gauge groups and a model with n T = 0, as well as some non-supersymmetric heterotic models, showing that the constraints arising from Dai-Freed anomaly cancellation extend beyond the lamppost of supersymmetry along the lines of [38]. The upshot of our analysis shows that the cancellation of Dai-Freed anomalies excludes some theories that were not previously ruled out, up to an assumption on the structure of the anomaly theory which we will specify.…”

Rigid vacua with Brane Supersymmetry Breaking

“…6 In the following, we shall restrict the discussion to perturbative anomalies. It would be interesting to study the role of Dai-Freed anomalies [41] along the lines of [42][43][44][45]. 7 Clearly, the factorisation of the anomaly polynomial is not unique, and other choices can make manifest the self-duality of the lattice.…”