A new SU(2) anomaly
© 2019 Author(s). A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly th...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/132545 |
| _version_ | 1826198550967484416 |
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| author | Wang, Juven Wen, Xiao-Gang Witten, Edward |
| author_facet | Wang, Juven Wen, Xiao-Gang Witten, Edward |
| author_sort | Wang, Juven |
| collection | MIT |
| description | © 2019 Author(s). A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons transform with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r + 3/2, is inconsistent. The theory is consistent if one picks a spin or spin c structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of "all-fermion electrodynamics." Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r + 3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is (-1)-Yw2w3. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions. |
| first_indexed | 2024-09-23T11:06:38Z |
| format | Article |
| id | mit-1721.1/132545 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:06:38Z |
| publishDate | 2021 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1325452021-09-21T03:44:51Z A new SU(2) anomaly Wang, Juven Wen, Xiao-Gang Witten, Edward © 2019 Author(s). A familiar anomaly affects SU(2) gauge theory in four dimensions: a theory with an odd number of fermion multiplets in the spin 1/2 representation of the gauge group, and more generally in representations of spin 2r + 1/2, is inconsistent. We describe here a more subtle anomaly that can affect SU(2) gauge theory in four dimensions under the condition that fermions transform with half-integer spin under SU(2) and bosons transform with integer spin. Such a theory, formulated in a way that requires no choice of spin structure, and with an odd number of fermion multiplets in representations of spin 4r + 3/2, is inconsistent. The theory is consistent if one picks a spin or spin c structure. Under Higgsing to U(1), the new SU(2) anomaly reduces to a known anomaly of "all-fermion electrodynamics." Like that theory, an SU(2) theory with an odd number of fermion multiplets in representations of spin 4r + 3/2 can provide a boundary state for a five-dimensional gapped theory whose partition function on a closed five-manifold Y is (-1)-Yw2w3. All statements have analogs with SU(2) replaced by Sp(2N). There is also an analog in five dimensions. 2021-09-20T18:22:58Z 2021-09-20T18:22:58Z 2020-11-16T19:10:23Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132545 en 10.1063/1.5082852 Journal of Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf AIP Publishing arXiv |
| spellingShingle | Wang, Juven Wen, Xiao-Gang Witten, Edward A new SU(2) anomaly |
| title | A new SU(2) anomaly |
| title_full | A new SU(2) anomaly |
| title_fullStr | A new SU(2) anomaly |
| title_full_unstemmed | A new SU(2) anomaly |
| title_short | A new SU(2) anomaly |
| title_sort | new su 2 anomaly |
| url | https://hdl.handle.net/1721.1/132545 |
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