Derived functors of the divided power functors

Breen, Lawrence; Mikhailov, Roman; Touzé, Antoine

doi:10.2140/gt.2016.20.257

Cited by 12 publications

(15 citation statements)

References 23 publications

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“…E.6 E 8 BE 8 and KpZ, 4q are homotopically equivalent in degrees less than 16, so Ω spin 7 pBE 8 q » Ω spin 7 pKpZ, 4qq. The homology of KpZ, 4q is given by [68] H ‚ pKpZ, 4q; Zq "¨0 There is a single potential obstruction in E 2 6,1 » H 6 pKpZ, 4q; Z 2 q, with generator the dual of Sq 2 ι. This generator is therefore not in the kernel of d 2 6,1 and is killed by the spectral sequence.…”

Section: E4 Sppnqmentioning

confidence: 99%

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

Monnier

Moore

2019

Commun. Math. Phys.

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We construct the Green-Schwarz terms of six-dimensional supergravity theories on spacetimes with non-trivial topology and gauge bundle. We prove the cancellation of all global gauge and gravitational anomalies for theories with gauge groups given by products of U pnq, SU pnq and Sppnq factors, as well as for E 8 . For other gauge groups, anomaly cancellation is equivalent to the triviality of a certain 7-dimensional spin topological field theory. We show in the case of a finite Abelian gauge group that there are residual global anomalies imposing constraints on the 6d supergravity. These constraints are compatible with the known F-theory models. Interestingly, our construction requires that the gravitational anomaly coefficient of the 6d supergravity theory is a characteristic element of the lattice of string charges, a fact true in six-dimensional F-theory compactifications but that until now was lacking a low-energy explanation. We also discover a new anomaly coefficient associated with a torsion characteristic class in theories with a disconnected gauge group.

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Section: E4 Sppnqmentioning

confidence: 99%

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

Monnier

Moore

2019

Commun. Math. Phys.

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“…Low degree homology groups of KpZ, 4q with integral coefficients are given for instance the Appendix C of [42]. We use the universal coefficient theorem to deduce from them the low degree cohomology with integral coefficients H ‚ pKpZ, 4q; Zq "¨0 1 2 3 4 5 6…”

Section: D2 the Integral Homology Of Fmentioning

confidence: 99%

The anomaly field theories of six-dimensional $(2,0)$ superconformal theories

Monnier

2018

Advances in Theoretical and Mathematical Physics

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“…The second page of the Atiyah-Hirzebruch spectral sequence corresponding to the fibration (4.42). The entries relevant to the computation of Ω Spin BG SM /Γ 6 ) are highlighted, all of which vanish already on the second page.These groups only feature factors of Z and Z/2, and the homology groups of the Eilenberg-Maclane space K(Z/3, 2) valued in Z and Z/2 are[39] i (K(Z/3, 2); Z) Z 0 Z/3 0 Z/3 0 H i (K(Z/3, 2); Z/2) Z/2 0…”

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confidence: 99%

Global anomalies in the Standard Model(s) and beyond

Davighi

Gripaios

Lohitsiri

2020

J. High Energ. Phys.

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We analyse global anomalies and related constraints in the Standard Model (SM) and various Beyond the Standard Model (BSM) theories. We begin by considering four distinct, but equally valid, versions of the SM, in which the gauge group is taken to be G = G SM /Γ n , with G SM = SU(3) × SU(2) × U(1) and Γ n isomorphic to Z/n where n ∈ {1, 2, 3, 6}. In addition to deriving constraints on the hypercharges of fields transforming in arbitrary representations of the SU(3) × SU(2) factor, we study the possibility of global anomalies in theories with these gauge groups by computing the bordism groups Ω Spin 5 (BG) using the Atiyah-Hirzebruch spectral sequence. In two cases we show that there are no global anomalies beyond the Witten anomaly, while in the other cases we show that there are no global anomalies at all, illustrating the subtle interplay between local and global anomalies. While freedom from global anomalies has been previously shown for the specific fermion content of the SM by embedding the SM in an anomaly-free SU(5) GUT, our results here remain true when the SM fermion content is extended arbitrarily. Going beyond the SM gauge groups, we show that there are no new global anomalies in extensions of the (usual) SM gauge group by U(1) m for any integer m, which correspond to phenomenologically well-motivated BSM theories featuring multiple Z bosons. Nor do we find any new global anomalies in various grand unified theories, including Pati-Salam and trinification models. We also consider global anomalies in a family of theories with gauge group SU(N) × Sp(M) × U(1), which share the phase structure of the SM for certain (N, M). Lastly, we discuss a BSM theory in which the SM fermions are defined using a spin c structure, for example by gauging B − L. Such a theory may be extended to all orientable four-manifolds, and we find no global anomalies.

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Derived functors of the divided power functors

Cited by 12 publications

References 23 publications

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

Remarks on the Green–Schwarz Terms of Six-Dimensional Supergravity Theories

The anomaly field theories of six-dimensional $(2,0)$ superconformal theories

Global anomalies in the Standard Model(s) and beyond

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