2-Group global symmetries and anomalies in six-dimensional quantum field theories
Abstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f (2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ∼ ∗...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-04-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP04(2021)252 |
| _version_ | 1818865793685782528 |
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| author | Clay Córdova Thomas T. Dumitrescu Kenneth Intriligator |
| author_facet | Clay Córdova Thomas T. Dumitrescu Kenneth Intriligator |
| author_sort | Clay Córdova |
| collection | DOAJ |
| description | Abstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f (2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ∼ ∗Tr (f (2) ∧ f (2)). We show that suitable mixed anomalies involving the gauge field f (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0. |
| first_indexed | 2024-12-19T10:53:12Z |
| format | Article |
| id | doaj.art-2aa2124f551d40dd833e98a24cf64649 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-19T10:53:12Z |
| publishDate | 2021-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2aa2124f551d40dd833e98a24cf646492022-12-21T20:24:54ZengSpringerOpenJournal of High Energy Physics1029-84792021-04-012021414610.1007/JHEP04(2021)2522-Group global symmetries and anomalies in six-dimensional quantum field theoriesClay Córdova0Thomas T. Dumitrescu1Kenneth Intriligator2Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of ChicagoMani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of CaliforniaDepartment of Physics, University of CaliforniaAbstract We examine six-dimensional quantum field theories through the lens of higher-form global symmetries. Every Yang-Mills gauge theory in six dimensions, with field strength f (2), naturally gives rise to a continuous 1-form global symmetry associated with the 2-form instanton current J (2) ∼ ∗Tr (f (2) ∧ f (2)). We show that suitable mixed anomalies involving the gauge field f (2) and ordinary 0-form global symmetries, such as flavor or Poincaré symmetries, lead to continuous 2-group global symmetries, which allow two flavor currents or two stress tensors to fuse into the 2-form current J (2). We discuss several features of 2-group symmetry in six dimensions, many of which parallel the four-dimensional case. The majority of six-dimensional supersymmetric conformal field theories (SCFTs) and little string theories have infrared phases with non-abelian gauge fields. We show that the mixed anomalies leading to 2-group symmetries can be present in little string theories, but that they are necessarily absent in SCFTs. This allows us to establish a previously conjectured algorithm for computing the ’t Hooft anomalies of most SCFTs from the spectrum of weakly-coupled massless particles on the tensor branch of these theories. We then apply this understanding to prove that the a-type Weyl anomaly of all SCFTs with a tensor branch must be positive, a > 0.https://doi.org/10.1007/JHEP04(2021)252Anomalies in Field and String TheoriesField Theories in Higher DimensionsRenormalization GroupSupersymmetric Gauge Theory |
| spellingShingle | Clay Córdova Thomas T. Dumitrescu Kenneth Intriligator 2-Group global symmetries and anomalies in six-dimensional quantum field theories Journal of High Energy Physics Anomalies in Field and String Theories Field Theories in Higher Dimensions Renormalization Group Supersymmetric Gauge Theory |
| title | 2-Group global symmetries and anomalies in six-dimensional quantum field theories |
| title_full | 2-Group global symmetries and anomalies in six-dimensional quantum field theories |
| title_fullStr | 2-Group global symmetries and anomalies in six-dimensional quantum field theories |
| title_full_unstemmed | 2-Group global symmetries and anomalies in six-dimensional quantum field theories |
| title_short | 2-Group global symmetries and anomalies in six-dimensional quantum field theories |
| title_sort | 2 group global symmetries and anomalies in six dimensional quantum field theories |
| topic | Anomalies in Field and String Theories Field Theories in Higher Dimensions Renormalization Group Supersymmetric Gauge Theory |
| url | https://doi.org/10.1007/JHEP04(2021)252 |
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