Anomaly Inflow and p-Form Gauge Theories

• Published in: Communications in mathematical physics 2022-04, Vol.391 (2), p.495-608
• Main Authors: Hsieh, Chang-Tse, Tachikawa, Yuji, Yonekura, Kazuya
• Format: Article
• Language: English
• Subjects: Anomalies; Branes; Classical and Quantum Gravitation; Complex Systems; Fermions; Gauge theory; Invariants; Mathematical and Computational Physics; Mathematical Physics; Partitions (mathematics); Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Theoretical; Topology
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-022-04333-w

Chiral and non-chiral p -form gauge fields have gravitational anomalies and anomalies of Green-Schwarz type. This means that they are most naturally realized as the boundary modes of bulk topological phases in one higher dimensions. We give a systematic description of the total bulk-boundary system which is analogous to the realization of a chiral fermion on the boundary of a massive fermion. The anomaly of the boundary theory is given by the partition function of the bulk theory, which we explicitly compute in terms of the Atiyah–Patodi–Singer η -invariant. We use our formalism to determine the SL ( 2 , Z ) anomaly of the 4d Maxwell theory. We also apply it to study the worldvolume theories of a single D-brane and an M5-brane in the presence of orientifolds, orbifolds, and S-folds in string, M, and F theories. In an appendix we also describe a simple class of non-unitary invertible topological theories whose partition function is not a bordism invariant, illustrating the necessity of the unitarity condition in the cobordism classification of the invertible phases.