Non-invertible symmetry in Calabi-Yau conformal field theories
Abstract We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our app...
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| Format: | Article |
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2025-01-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP01(2025)045 |
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| author | Clay Córdova Giovanni Rizi |
| author_facet | Clay Córdova Giovanni Rizi |
| author_sort | Clay Córdova |
| collection | DOAJ |
| description | Abstract We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point. |
| format | Article |
| id | doaj-art-795b2d3d398842fcb5150d2ce62dc11b |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-795b2d3d398842fcb5150d2ce62dc11b2025-01-19T12:07:05ZengSpringerOpenJournal of High Energy Physics1029-84792025-01-012025116610.1007/JHEP01(2025)045Non-invertible symmetry in Calabi-Yau conformal field theoriesClay Córdova0Giovanni Rizi1Kadanoff Center for Theoretical Physics & Enrico Fermi Institute, University of ChicagoSISSAAbstract We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point.https://doi.org/10.1007/JHEP01(2025)045Discrete SymmetriesGlobal SymmetriesField Theories in Lower DimensionsSigma Models |
| spellingShingle | Clay Córdova Giovanni Rizi Non-invertible symmetry in Calabi-Yau conformal field theories Journal of High Energy Physics Discrete Symmetries Global Symmetries Field Theories in Lower Dimensions Sigma Models |
| title | Non-invertible symmetry in Calabi-Yau conformal field theories |
| title_full | Non-invertible symmetry in Calabi-Yau conformal field theories |
| title_fullStr | Non-invertible symmetry in Calabi-Yau conformal field theories |
| title_full_unstemmed | Non-invertible symmetry in Calabi-Yau conformal field theories |
| title_short | Non-invertible symmetry in Calabi-Yau conformal field theories |
| title_sort | non invertible symmetry in calabi yau conformal field theories |
| topic | Discrete Symmetries Global Symmetries Field Theories in Lower Dimensions Sigma Models |
| url | https://doi.org/10.1007/JHEP01(2025)045 |
| work_keys_str_mv | AT claycordova noninvertiblesymmetryincalabiyauconformalfieldtheories AT giovannirizi noninvertiblesymmetryincalabiyauconformalfieldtheories |