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

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 ( n ), SU ( n ) and Sp ( n ) factors...

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Bibliographic Details
Published in:Communications in mathematical physics 2019-12, Vol.372 (3), p.963-1025
Main Authors: Monnier, Samuel, Moore, Gregory W.
Format: Article
Language:English
Subjects:
Anomalies
Classical and Quantum Gravitation
Complex Systems
Field theory
Gravitation theory
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Supergravity
Theoretical
Topology
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Summary: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 ( n ), SU ( n ) and Sp ( n ) 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03341-7