Anomaly inflow and $p$-form gauge theories
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| Format: | Preprint |
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2020
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| _version_ | 1866914178992701440 |
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| author | Hsieh, Chang-Tse Tachikawa, Yuji Yonekura, Kazuya |
| author_facet | Hsieh, Chang-Tse Tachikawa, Yuji Yonekura, Kazuya |
| contents | 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 $\mathrm{SL}(2,{\mathbb Z})$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2003_11550 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Anomaly inflow and $p$-form gauge theories Hsieh, Chang-Tse Tachikawa, Yuji Yonekura, Kazuya High Energy Physics - Theory Strongly Correlated Electrons 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 $\mathrm{SL}(2,{\mathbb Z})$ 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. |
| title | Anomaly inflow and $p$-form gauge theories |
| topic | High Energy Physics - Theory Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2003.11550 |