D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants
Abstract We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2023)045 |
| _version_ | 1797341366324297728 |
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| author | Jin Chen Yongchao Lü Xin Wang |
| author_facet | Jin Chen Yongchao Lü Xin Wang |
| author_sort | Jin Chen |
| collection | DOAJ |
| description | Abstract We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov-Shatashvili limit, the 6d partition function with insertions of codimension two and four defects serve as the eigenfunction and eigenvalues of the difference equation, respectively. We further identify the quantum curve of D-type minimal conformal matters with an elliptic Garnier system recently studied in the integrability community. At last, as a concrete consequence of our elliptic quantum curve, we study its RG flows to obtain various quantum curves of 5d Sp(N) + N f F, N f ≤ 2N + 5 theories. |
| first_indexed | 2024-03-08T10:18:00Z |
| format | Article |
| id | doaj.art-ae68028fb14a4f62bbc02294db3edcd6 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:18:00Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-ae68028fb14a4f62bbc02294db3edcd62024-01-28T12:21:45ZengSpringerOpenJournal of High Energy Physics1029-84792023-10-0120231014710.1007/JHEP10(2023)045D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendantsJin Chen0Yongchao Lü1Xin Wang2Department of Physics, Xiamen UniversitySchool of Physics, Korea Institute for Advanced StudyQuantum Universe Center, Korea Institute for Advanced StudyAbstract We study the quantization of the 6d Seiberg-Witten curve for D-type minimal conformal matter theories compactified on a two-torus. The quantized 6d curve turns out to be a difference equation established via introducing codimension two and four surface defects. We show that, in the Nekrasov-Shatashvili limit, the 6d partition function with insertions of codimension two and four defects serve as the eigenfunction and eigenvalues of the difference equation, respectively. We further identify the quantum curve of D-type minimal conformal matters with an elliptic Garnier system recently studied in the integrability community. At last, as a concrete consequence of our elliptic quantum curve, we study its RG flows to obtain various quantum curves of 5d Sp(N) + N f F, N f ≤ 2N + 5 theories.https://doi.org/10.1007/JHEP10(2023)045Field Theories in Higher DimensionsNonperturbative EffectsSupersymmetric Gauge TheorySupersymmetry and Duality |
| spellingShingle | Jin Chen Yongchao Lü Xin Wang D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants Journal of High Energy Physics Field Theories in Higher Dimensions Nonperturbative Effects Supersymmetric Gauge Theory Supersymmetry and Duality |
| title | D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants |
| title_full | D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants |
| title_fullStr | D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants |
| title_full_unstemmed | D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants |
| title_short | D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants |
| title_sort | d type minimal conformal matter quantum curves elliptic garnier systems and the 5d descendants |
| topic | Field Theories in Higher Dimensions Nonperturbative Effects Supersymmetric Gauge Theory Supersymmetry and Duality |
| url | https://doi.org/10.1007/JHEP10(2023)045 |
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