Anomaly Inflow and p-Form Gauge Theories
Journal
Communications in Mathematical Physics
Journal Volume
391
Journal Issue
2
Pages
495-608
Date Issued
2022
Author(s)
Abstract
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. © 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
Publisher
Springer Science and Business Media Deutschland GmbH
Type
journal article