期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 11, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP11(2021)142
关键词
Anomalies in Field and String Theories; Field Theories in Lower Dimensions; Global Symmetries; Topological Field Theories
资金
- Government of Canada through the Department of Innovation, Science and Economic Development Canada
- Province of Ontario through the Ministry of Colleges and Universities
We demonstrate that global anomalies can be detected by analyzing the way the symmetry algebra is realized in the torus Hilbert space of the anomalous theory. Anomalies may imply an exact bose-fermi degeneracy in the Hilbert space, revealing a supersymmetric spectrum of states.
We show that certain global anomalies can be detected in an elementary fashion by analyzing the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory. Distinct anomalous behaviours imprinted in the Hilbert space are identified with the distinct cohomology layers that appear in the classification of anomalies in terms of cobordism groups. We illustrate the manifestation of the layers in the Hilbert for a variety of anomalous symmetries and spacetime dimensions, including time-reversal symmetry, and both in systems of fermions and in anomalous topological quantum field theories (TQFTs) in 2+1d. We argue that anomalies can imply an exact bose-fermi degeneracy in the Hilbert space, thus revealing a supersymmetric spectrum of states; we provide a sharp characterization of when this phenomenon occurs and give nontrivial examples in various dimensions, including in strongly coupled QFTs. Unraveling the anomalies of TQFTs leads us to develop the construction of the Hilbert spaces, the action of operators and the modular data in spin TQFTs, material that can be read on its own.
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