期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 11, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP11(2022)050
关键词
Anomalies in Field and String Theories; Field Theories in Higher Dimensions; Global Symmetries; Topological Field Theories
资金
- Albert Einstein Center for fundamental physics at Bern university
- Swiss National Science Foundation
- European Union
- European Union's Horizon 2020 Framework: ERC grant [682608]
This article discusses the symmetry TFT of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet, and explores the coupling of higher-form symmetries, mixed anomalies, and the fate of 2-form and 1-form symmetries when coupled to gravity.
Symmetries and anomalies of a d-dimensional quantum field theory are often encoded in a (d + 1)-dimensional topological action, called symmetry topological field theory (TFT). We derive the symmetry TFT for the 2-form and 1-form symmetries of 6d (1, 0) field theories, focusing on theories with a single tensor multiplet (rank 1). We implement this by coupling the low-energy tensor branch action to the background fields for the higher-form symmetries and by looking at the symmetry transformation rules on dynamical and background fields. These transformation rules also imply a mixing of the higher-form symmetries in a 3-group structure. For some specific and related higher rank cases, we also derive the symmetry TFT from the holographic dual IIA supergravity solutions. The symmetry TFT action contains a coupling between the 2-form symmetry and the 1-form symmetry backgrounds, which leads to a mixed anomaly between the 1-form symmetries of the 5d KK-theory obtained by circle compactification. We confirm this by a pure 5d analysis provided by the 5d effective low-energy Coulomb branch Lagrangian coupled to background fields. We also derive the symmetry TFT for 5d SU(p) supersymmetric gauge theories with Chern-Simons level q and for 5d theories without non-abelian gauge theory description at low-energy. Finally, we discuss the fate of the 2-form and 1-form symmetry of rank 1 6d field theories when coupled to gravity.
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