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Modular differential equations with movable poles and admissible RCFT characters

Das, Arpit; Gowdigere, Chethan N.; Mukhi, Sunil; Santara, Jagannath

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Authors

Profile image of Arpit Das

Arpit Das arpit.das@durham.ac.uk
PGR Student Doctor of Philosophy

Chethan N. Gowdigere

Sunil Mukhi

Jagannath Santara



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.

Citation

Das, A., Gowdigere, C. N., Mukhi, S., & Santara, J. (2023). Modular differential equations with movable poles and admissible RCFT characters. Journal of High Energy Physics, 2023(12), Article 143. https://doi.org/10.1007/jhep12%282023%29143

Journal Article Type Article
Acceptance Date Dec 4, 2023
Online Publication Date Dec 20, 2023
Publication Date 2023-12
Deposit Date Jan 2, 2024
Publicly Available Date Jan 2, 2024
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Electronic ISSN 1029-8479
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2023
Issue 12
Article Number 143
DOI https://doi.org/10.1007/jhep12%282023%29143
Keywords Scale and Conformal Symmetries, Conformal and W Symmetry
Public URL https://durham-repository.worktribe.com/output/2049633

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