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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Main Authors: Arun Debray, Sanath K. Devalapurkar, Cameron Krulewski, Yu Leon Liu, Natalia Pacheco-Tallaj, Ryan Thorngren
Format: Article
Language:English
Published: SpringerOpen 2025-07-01
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.
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institution Kabale University
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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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