Anomalies and symmetry fractionalization
We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct cho...
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| Format: | Article |
| Language: | English |
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SciPost
2023-09-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.3.079 |
| _version_ | 1797692285333274624 |
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| author | Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski |
| author_facet | Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski |
| author_sort | Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski |
| collection | DOAJ |
| description | We study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory. |
| first_indexed | 2024-03-12T02:26:21Z |
| format | Article |
| id | doaj.art-c765729b641d4ccfbc5e2f53eff195a8 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-12T02:26:21Z |
| publishDate | 2023-09-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-c765729b641d4ccfbc5e2f53eff195a82023-09-05T12:46:09ZengSciPostSciPost Physics2542-46532023-09-0115307910.21468/SciPostPhys.15.3.079Anomalies and symmetry fractionalizationDiego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar KomargodskiWe study ordinary, zero-form symmetry $G$ and its anomalies in a system with a one-form symmetry $\Gamma$. In a theory with one-form symmetry, the action of $G$ on charged line operators is not completely determined, and additional data, a fractionalization class, needs to be specified. Distinct choices of a fractionalization class can result in different values for the anomalies of $G$ if the theory has an anomaly involving $\Gamma$. Therefore, the computation of the 't Hooft anomaly for an ordinary symmetry $G$ generally requires first discovering the one-form symmetry $\Gamma$ of the physical system. We show that the multiple values of the anomaly for $G$ can be realized by twisted gauge transformations, since twisted gauge transformations shift fractionalization classes. We illustrate these ideas in QCD theories in diverse dimensions. We successfully match the anomalies of time-reversal symmetries in $2+1d$ gauge theories, across the different fractionalization classes, with previous conjectures for the infrared phases of such strongly coupled theories, and also provide new checks of these proposals. We perform consistency checks of recent proposals about two-dimensional adjoint QCD and present new results about the anomaly of the axial $\mathbb{Z}_{2N}$ symmetry in $3+1d$ ${\cal N}=1$ super-Yang-Mills. Finally, we study fractionalization classes that lead to 2-group symmetry, both in QCD-like theories, and in $2+1d$ $\mathbb{Z}_2$ gauge theory.https://scipost.org/SciPostPhys.15.3.079 |
| spellingShingle | Diego Delmastro, Jaume Gomis, Po-Shen Hsin, Zohar Komargodski Anomalies and symmetry fractionalization SciPost Physics |
| title | Anomalies and symmetry fractionalization |
| title_full | Anomalies and symmetry fractionalization |
| title_fullStr | Anomalies and symmetry fractionalization |
| title_full_unstemmed | Anomalies and symmetry fractionalization |
| title_short | Anomalies and symmetry fractionalization |
| title_sort | anomalies and symmetry fractionalization |
| url | https://scipost.org/SciPostPhys.15.3.079 |
| work_keys_str_mv | AT diegodelmastrojaumegomisposhenhsinzoharkomargodski anomaliesandsymmetryfractionalization |