TY - JOUR

T1 - Anomaly Inflow and p-Form Gauge Theories

AU - Hsieh, Chang Tse

AU - Tachikawa, Yuji

AU - Yonekura, Kazuya

N1 - Funding Information:
CTH and YT are in part supported by WPI Initiative, MEXT, Japan at IPMU, the University of Tokyo. CTH is also supported in part by JSPS KAKENHI Grant-in-Aid (Early-Career Scientists), No.19K14608. YT is also supported in part by JSPS KAKENHI Grant-in-Aid (Wakate-A), No.17H04837 and JSPS KAKENHI Grant-in-Aid (Kiban-S), No.16H06335. KY is supported by JSPS KAKENHI Grant-in-Aid (Wakate-B), No.17K14265.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-022-04333-w

DO - 10.1007/s00220-022-04333-w

M3 - Article

AN - SCOPUS:85125519641

SN - 0010-3616

VL - 391

SP - 495

EP - 608

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -