Anomaly inflow and holography
Abstract We systematically study the perturbative anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime (AdS5). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-05-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP05(2021)072 |
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| author | Sungwoo Hong Gabriele Rigo |
| author_facet | Sungwoo Hong Gabriele Rigo |
| author_sort | Sungwoo Hong |
| collection | DOAJ |
| description | Abstract We systematically study the perturbative anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime (AdS5). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including weakly gauging and spontaneous symmetry breaking of the global symmetries of the dual 4D CFT. Our main contribution is to provide a unified and comprehensive discussion of the subject, together with a detailed description of the dual CFT picture for each case. To this end, we employ a gauge-fixed effective action suitable for a holographic study, which allows us to incorporate general UV and IR boundary conditions (BCs). As part of the process, we reproduce many known results in the literature, such as ’t Hooft anomaly matching for unbroken symmetry (Neumann IR-BC) and (gauged) Wess-Zumino-Witten (WZW) action for broken symmetry (IR-BC breaks the bulk group G → H). In addition, we show that anomaly matching occurs for ABJ anomalies as well as ’t Hooft anomalies, which suggests anomalies inflowed from the bulk CS theory are necessarily free of mixed anomalies with the confining gauge force of the 4D dual CFT. In the case of broken symmetry, we prove that the “would-be” Goldstone bosons associated with the weakly gauged symmetry are completely removed by a proper field redefinition, provided the anomaly from the bulk is exactly cancelled by the boundary contribution, hence confirming the standard expectation. Moreover, we present a holographic formulation of Witten’s argument for the quantization condition for the WZW action, and argue in favor of an alternative way to obtain the same condition using a “deformed” theory (different BCs). We work out several examples, including a product group with mixed anomaly, and identify the corresponding dual CFT picture. We consider a fully general case typically arising in the context of dynamical electroweak symmetry breaking. |
| first_indexed | 2024-12-20T01:33:51Z |
| format | Article |
| id | doaj.art-38d61e785183441d851d4562b0f61e05 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-20T01:33:51Z |
| publishDate | 2021-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-38d61e785183441d851d4562b0f61e052022-12-21T19:58:04ZengSpringerOpenJournal of High Energy Physics1029-84792021-05-012021515010.1007/JHEP05(2021)072Anomaly inflow and holographySungwoo Hong0Gabriele Rigo1Department of Physics, LEPP, Cornell UniversityDepartment of Physics, Syracuse UniversityAbstract We systematically study the perturbative anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime (AdS5). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including weakly gauging and spontaneous symmetry breaking of the global symmetries of the dual 4D CFT. Our main contribution is to provide a unified and comprehensive discussion of the subject, together with a detailed description of the dual CFT picture for each case. To this end, we employ a gauge-fixed effective action suitable for a holographic study, which allows us to incorporate general UV and IR boundary conditions (BCs). As part of the process, we reproduce many known results in the literature, such as ’t Hooft anomaly matching for unbroken symmetry (Neumann IR-BC) and (gauged) Wess-Zumino-Witten (WZW) action for broken symmetry (IR-BC breaks the bulk group G → H). In addition, we show that anomaly matching occurs for ABJ anomalies as well as ’t Hooft anomalies, which suggests anomalies inflowed from the bulk CS theory are necessarily free of mixed anomalies with the confining gauge force of the 4D dual CFT. In the case of broken symmetry, we prove that the “would-be” Goldstone bosons associated with the weakly gauged symmetry are completely removed by a proper field redefinition, provided the anomaly from the bulk is exactly cancelled by the boundary contribution, hence confirming the standard expectation. Moreover, we present a holographic formulation of Witten’s argument for the quantization condition for the WZW action, and argue in favor of an alternative way to obtain the same condition using a “deformed” theory (different BCs). We work out several examples, including a product group with mixed anomaly, and identify the corresponding dual CFT picture. We consider a fully general case typically arising in the context of dynamical electroweak symmetry breaking.https://doi.org/10.1007/JHEP05(2021)072AdS-CFT CorrespondenceAnomalies in Field and String TheoriesChern-Simons TheoriesField Theories in Higher Dimensions |
| spellingShingle | Sungwoo Hong Gabriele Rigo Anomaly inflow and holography Journal of High Energy Physics AdS-CFT Correspondence Anomalies in Field and String Theories Chern-Simons Theories Field Theories in Higher Dimensions |
| title | Anomaly inflow and holography |
| title_full | Anomaly inflow and holography |
| title_fullStr | Anomaly inflow and holography |
| title_full_unstemmed | Anomaly inflow and holography |
| title_short | Anomaly inflow and holography |
| title_sort | anomaly inflow and holography |
| topic | AdS-CFT Correspondence Anomalies in Field and String Theories Chern-Simons Theories Field Theories in Higher Dimensions |
| url | https://doi.org/10.1007/JHEP05(2021)072 |
| work_keys_str_mv | AT sungwoohong anomalyinflowandholography AT gabrielerigo anomalyinflowandholography |