Anomaly inflow and $p$-form gauge theories

Fuente: arXiv
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Main Authors: Hsieh, Chang-Tse, Tachikawa, Yuji, Yonekura, Kazuya
Format: Preprint
Published: 2020
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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
id 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