A note on defect stability in d = 4 − ε
Abstract We explore the space of scalar line, surface and interface defect field theories in d = 4 − ε by examining their stability properties under generic deformations. Examples are known of multiple stable line defect Conformal Field Theories (dCFTs) existing simultaneously, unlike the case of no...
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| Format: | Article |
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2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)187 |
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| author | William H. Pannell |
| author_facet | William H. Pannell |
| author_sort | William H. Pannell |
| collection | DOAJ |
| description | Abstract We explore the space of scalar line, surface and interface defect field theories in d = 4 − ε by examining their stability properties under generic deformations. Examples are known of multiple stable line defect Conformal Field Theories (dCFTs) existing simultaneously, unlike the case of normal multiscalar field theories where a theorem by Michel guarantees that the stable fixed point is the unique global minimum of a so-called A-function. We prove that a suitable modification of Michel’s theorem survives for line defect theories, with fixed points locally rather than globally minimizing an A-function along a specified surface in coupling space and provide a novel classification of the fixed points in the hypertetrahedral line defect model. For surface defects Michel’s theorem survives almost untouched, and we explore bulk models for which the symmetry preserving defect is the unique stable point. For interface defects we prove only the weaker condition that there exist no fixed points stable against generic deformations for N ≥ 6. |
| format | Article |
| id | doaj-art-d1eed7529d8843f29c32c3add2c5160e |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d1eed7529d8843f29c32c3add2c5160e2025-01-05T12:06:32ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213610.1007/JHEP12(2024)187A note on defect stability in d = 4 − εWilliam H. Pannell0Department of Mathematics, King’s College London, StrandAbstract We explore the space of scalar line, surface and interface defect field theories in d = 4 − ε by examining their stability properties under generic deformations. Examples are known of multiple stable line defect Conformal Field Theories (dCFTs) existing simultaneously, unlike the case of normal multiscalar field theories where a theorem by Michel guarantees that the stable fixed point is the unique global minimum of a so-called A-function. We prove that a suitable modification of Michel’s theorem survives for line defect theories, with fixed points locally rather than globally minimizing an A-function along a specified surface in coupling space and provide a novel classification of the fixed points in the hypertetrahedral line defect model. For surface defects Michel’s theorem survives almost untouched, and we explore bulk models for which the symmetry preserving defect is the unique stable point. For interface defects we prove only the weaker condition that there exist no fixed points stable against generic deformations for N ≥ 6.https://doi.org/10.1007/JHEP12(2024)187Renormalization and RegularizationRenormalization Group |
| spellingShingle | William H. Pannell A note on defect stability in d = 4 − ε Journal of High Energy Physics Renormalization and Regularization Renormalization Group |
| title | A note on defect stability in d = 4 − ε |
| title_full | A note on defect stability in d = 4 − ε |
| title_fullStr | A note on defect stability in d = 4 − ε |
| title_full_unstemmed | A note on defect stability in d = 4 − ε |
| title_short | A note on defect stability in d = 4 − ε |
| title_sort | note on defect stability in d 4 ε |
| topic | Renormalization and Regularization Renormalization Group |
| url | https://doi.org/10.1007/JHEP12(2024)187 |
| work_keys_str_mv | AT williamhpannell anoteondefectstabilityind4e AT williamhpannell noteondefectstabilityind4e |