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

• Published in: Communications in mathematical physics Vol. 372; no. 3; pp. 963 - 1025
• Main Authors: Monnier, Samuel, Moore, Gregory W.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019; Springer Nature B.V
• 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
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-019-03341-7

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.