A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
Abstract We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symm...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-07-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP07(2025)007 |
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| author | Arun Debray Sanath K. Devalapurkar Cameron Krulewski Yu Leon Liu Natalia Pacheco-Tallaj Ryan Thorngren |
| author_facet | Arun Debray Sanath K. Devalapurkar Cameron Krulewski Yu Leon Liu Natalia Pacheco-Tallaj Ryan Thorngren |
| author_sort | Arun Debray |
| collection | DOAJ |
| description | Abstract We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES). The mathematical backbone of the SBLES is studied in a companion paper [1]. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases. |
| format | Article |
| id | doaj-art-29e20afd0a294d8498b1a1d6858ce8d3 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-29e20afd0a294d8498b1a1d6858ce8d32025-08-20T03:42:45ZengSpringerOpenJournal of High Energy Physics1029-84792025-07-012025714810.1007/JHEP07(2025)007A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phasesArun Debray0Sanath K. Devalapurkar1Cameron Krulewski2Yu Leon Liu3Natalia Pacheco-Tallaj4Ryan Thorngren5Department of Mathematics, Purdue UniversityHarvard University Department of MathematicsMassachusetts Institute of Technology, Department of MathematicsHarvard University Department of MathematicsMassachusetts Institute of Technology, Department of MathematicsMani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of CaliforniaAbstract We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations which sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects, and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES). The mathematical backbone of the SBLES is studied in a companion paper [1]. Our work further develops the theory of higher Berry phase and its bulk-boundary correspondence, and serves as a new computational tool for classifying symmetry protected topological phases.https://doi.org/10.1007/JHEP07(2025)007Anomalies in Field and String TheoriesTopological Field Theories |
| spellingShingle | Arun Debray Sanath K. Devalapurkar Cameron Krulewski Yu Leon Liu Natalia Pacheco-Tallaj Ryan Thorngren A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases Journal of High Energy Physics Anomalies in Field and String Theories Topological Field Theories |
| title | A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases |
| title_full | A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases |
| title_fullStr | A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases |
| title_full_unstemmed | A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases |
| title_short | A long exact sequence in symmetry breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases |
| title_sort | long exact sequence in symmetry breaking order parameter constraints defect anomaly matching and higher berry phases |
| topic | Anomalies in Field and String Theories Topological Field Theories |
| url | https://doi.org/10.1007/JHEP07(2025)007 |
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