Modular differential equations with movable poles and admissible RCFT characters
Abstract Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast terr...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-12-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP12(2023)143 |
| _version_ | 1827301369734758400 |
|---|---|
| author | Arpit Das Chethan N. Gowdigere Sunil Mukhi Jagannath Santara |
| author_facet | Arpit Das Chethan N. Gowdigere Sunil Mukhi Jagannath Santara |
| author_sort | Arpit Das |
| collection | DOAJ |
| description | Abstract Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach. |
| first_indexed | 2024-03-08T19:49:02Z |
| format | Article |
| id | doaj.art-113305d277f9403b8250acd0f7c485ef |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-24T16:21:59Z |
| publishDate | 2023-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-113305d277f9403b8250acd0f7c485ef2024-03-31T11:07:37ZengSpringerOpenJournal of High Energy Physics1029-84792023-12-0120231217210.1007/JHEP12(2023)143Modular differential equations with movable poles and admissible RCFT charactersArpit Das0Chethan N. Gowdigere1Sunil Mukhi2Jagannath Santara3Centre for Particle Theory, Department of Mathematical Sciences, Durham UniversityNational Institute of Science Education and Research BhubaneshwarTheoretical Physics Department, CERNDepartment of Physics, Indian Institute of Technology MadrasAbstract Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach.https://doi.org/10.1007/JHEP12(2023)143Conformal and W SymmetryScale and Conformal Symmetries |
| spellingShingle | Arpit Das Chethan N. Gowdigere Sunil Mukhi Jagannath Santara Modular differential equations with movable poles and admissible RCFT characters Journal of High Energy Physics Conformal and W Symmetry Scale and Conformal Symmetries |
| title | Modular differential equations with movable poles and admissible RCFT characters |
| title_full | Modular differential equations with movable poles and admissible RCFT characters |
| title_fullStr | Modular differential equations with movable poles and admissible RCFT characters |
| title_full_unstemmed | Modular differential equations with movable poles and admissible RCFT characters |
| title_short | Modular differential equations with movable poles and admissible RCFT characters |
| title_sort | modular differential equations with movable poles and admissible rcft characters |
| topic | Conformal and W Symmetry Scale and Conformal Symmetries |
| url | https://doi.org/10.1007/JHEP12(2023)143 |
| work_keys_str_mv | AT arpitdas modulardifferentialequationswithmovablepolesandadmissiblercftcharacters AT chethanngowdigere modulardifferentialequationswithmovablepolesandadmissiblercftcharacters AT sunilmukhi modulardifferentialequationswithmovablepolesandadmissiblercftcharacters AT jagannathsantara modulardifferentialequationswithmovablepolesandadmissiblercftcharacters |