Global anomalies on the Hilbert space

Abstract 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 “...

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Autores principales:	Diego Delmastro, Davide Gaiotto, Jaume Gomis
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Anomalies in Field and String Theories Field Theories in Lower Dimensions Global Symmetries Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/96cb761f72ac4ba5acd879783ffc8d5e
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spelling	oai:doaj.org-article:96cb761f72ac4ba5acd879783ffc8d5e2021-11-21T12:41:35ZGlobal anomalies on the Hilbert space10.1007/JHEP11(2021)1421029-8479https://doaj.org/article/96cb761f72ac4ba5acd879783ffc8d5e2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)142https://doaj.org/toc/1029-8479Abstract 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.Diego DelmastroDavide GaiottoJaume GomisSpringerOpenarticleAnomalies in Field and String TheoriesField Theories in Lower DimensionsGlobal SymmetriesTopological Field TheoriesNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-68 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Anomalies in Field and String Theories Field Theories in Lower Dimensions Global Symmetries Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Anomalies in Field and String Theories Field Theories in Lower Dimensions Global Symmetries Topological Field Theories Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Diego Delmastro Davide Gaiotto Jaume Gomis Global anomalies on the Hilbert space
description	Abstract 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.
format	article
author	Diego Delmastro Davide Gaiotto Jaume Gomis
author_facet	Diego Delmastro Davide Gaiotto Jaume Gomis
author_sort	Diego Delmastro
title	Global anomalies on the Hilbert space
title_short	Global anomalies on the Hilbert space
title_full	Global anomalies on the Hilbert space
title_fullStr	Global anomalies on the Hilbert space
title_full_unstemmed	Global anomalies on the Hilbert space
title_sort	global anomalies on the hilbert space
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/96cb761f72ac4ba5acd879783ffc8d5e
work_keys_str_mv	AT diegodelmastro globalanomaliesonthehilbertspace AT davidegaiotto globalanomaliesonthehilbertspace AT jaumegomis globalanomaliesonthehilbertspace
_version_	1718418839377543168

Global anomalies on the Hilbert space

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