Hecke relations in rational conformal field theory
Abstract We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and fusion algebra of RCFTs to a relation between RCFT cha...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP09(2018)032 |
| _version_ | 1830513093347639296 |
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| author | Jeffrey A. Harvey Yuxiao Wu |
| author_facet | Jeffrey A. Harvey Yuxiao Wu |
| author_sort | Jeffrey A. Harvey |
| collection | DOAJ |
| description | Abstract We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and fusion algebra of RCFTs to a relation between RCFT characters. We apply our results to derive a number of relations between characters of known RCFTs with different central charges and also explore the relation between Hecke operators and RCFT characters as solutions to modular linear differential equations. We show that Hecke operators can be used to construct an infinite set of possible characters for RCFTs with two independent characters and increasing central charge. These characters have multiplicity one for the vacuum representation, positive integer coefficients in their q expansions, and are associated to a two-dimensional representation of the modular group which leads to non-negative integer fusion coefficients as determined by the Verlinde formula. |
| first_indexed | 2024-12-22T02:38:13Z |
| format | Article |
| id | doaj.art-cd25ffd67d32414cad064d7c7b56fc2f |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-22T02:38:13Z |
| publishDate | 2018-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-cd25ffd67d32414cad064d7c7b56fc2f2022-12-21T18:41:42ZengSpringerOpenJournal of High Energy Physics1029-84792018-09-012018913710.1007/JHEP09(2018)032Hecke relations in rational conformal field theoryJeffrey A. Harvey0Yuxiao Wu1Enrico Fermi Institute and Department of Physics, University of ChicagoEnrico Fermi Institute and Department of Physics, University of ChicagoAbstract We define Hecke operators on vector-valued modular forms of the type that appear as characters of rational conformal field theories (RCFTs). These operators extend the previously studied Galois symmetry of the modular representation and fusion algebra of RCFTs to a relation between RCFT characters. We apply our results to derive a number of relations between characters of known RCFTs with different central charges and also explore the relation between Hecke operators and RCFT characters as solutions to modular linear differential equations. We show that Hecke operators can be used to construct an infinite set of possible characters for RCFTs with two independent characters and increasing central charge. These characters have multiplicity one for the vacuum representation, positive integer coefficients in their q expansions, and are associated to a two-dimensional representation of the modular group which leads to non-negative integer fusion coefficients as determined by the Verlinde formula.http://link.springer.com/article/10.1007/JHEP09(2018)032Conformal Field Models in String TheoryConformal Field Theory |
| spellingShingle | Jeffrey A. Harvey Yuxiao Wu Hecke relations in rational conformal field theory Journal of High Energy Physics Conformal Field Models in String Theory Conformal Field Theory |
| title | Hecke relations in rational conformal field theory |
| title_full | Hecke relations in rational conformal field theory |
| title_fullStr | Hecke relations in rational conformal field theory |
| title_full_unstemmed | Hecke relations in rational conformal field theory |
| title_short | Hecke relations in rational conformal field theory |
| title_sort | hecke relations in rational conformal field theory |
| topic | Conformal Field Models in String Theory Conformal Field Theory |
| url | http://link.springer.com/article/10.1007/JHEP09(2018)032 |
| work_keys_str_mv | AT jeffreyaharvey heckerelationsinrationalconformalfieldtheory AT yuxiaowu heckerelationsinrationalconformalfieldtheory |