Anomaly Inflow and p-Form Gauge Theories

Chang Tse Hsieh, Yuji Tachikawa, Kazuya Yonekura

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)495-608
Number of pages114
JournalCommunications in Mathematical Physics
Issue number2
Publication statusPublished - 2022 Apr

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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