Non-Abelian Gauge Theories, Sigma Models, Higher Anomalies, Symmetries, and Cobordisms I: Classification of Higher-Symmetry Protected Topological States and Higher Anomalies via a generalized cobordism theory

Zheyan Wang USTC Juven Wang IAS Princeton

Mathematical Physics mathscidoc:1904.22013

We explore the higher-form generalized global symmetries and higher anomalies based on a generalized cobordism theory. Our cobordism calculation guides us to classify higher anomalies and topological terms for Yang-Mills (YM) gauge theories and sigma models in various dimensions. Some of YM gauge theories can be obtained from dynamically gauging the SU(N) time-reversal symmetric cobordism invariants (SU(N)-generalized topological superconductors/insulators [arXiv:1711.11587]). We elaborate the cases of YM theory with a compact Lie gauge group (such as SU(N) with N=2, 3 and others) particularly in a 4d spacetime. We provide the relevant homotopy and cobordism group calculations of higher classifying spaces, based on mathematical tools of algebraic topology, to support the physics stories.
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  • https://arxiv.org/abs/1812.11967
@inproceedings{zheyannon-abelian,
  title={Non-Abelian Gauge Theories, Sigma Models, Higher Anomalies, Symmetries, and Cobordisms I: Classification of Higher-Symmetry Protected Topological States and Higher Anomalies via a generalized cobordism theory},
  author={Zheyan Wang, and Juven Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428055001943795286},
}
Zheyan Wang, and Juven Wang. Non-Abelian Gauge Theories, Sigma Models, Higher Anomalies, Symmetries, and Cobordisms I: Classification of Higher-Symmetry Protected Topological States and Higher Anomalies via a generalized cobordism theory. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190428055001943795286.
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