Classifying three-character RCFTs with Wronskian index equalling 0 or 2

Abstract In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the charac...

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Autores principales:	Arpit Das, Chethan N. Gowdigere, Jagannath Santara
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Conformal and W Symmetry Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/b35b856ff6114ab985e641c8ceaa7bba
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spelling	oai:doaj.org-article:b35b856ff6114ab985e641c8ceaa7bba2021-11-28T12:39:34ZClassifying three-character RCFTs with Wronskian index equalling 0 or 210.1007/JHEP11(2021)1951029-8479https://doaj.org/article/b35b856ff6114ab985e641c8ceaa7bba2021-11-01T00:00:00Zhttps://doi.org/10.1007/JHEP11(2021)195https://doaj.org/toc/1029-8479Abstract In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and l, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study [3,0] and [3,2] MLDEs in order to classify the corresponding CFTs. We reduce the problem to a “finite” problem: to classify CFTs with central charge 0 < c ≤ 96, we need to perform 6, 720 computations for the former and 20, 160 for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity. In the [3,0] case, for 0 < c ≤ 96, we obtain many character-like solutions: two infinite classes and a discrete set of 303. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify [3,2] CFTs for 0 < c ≤ 96: each CFT in this case is obtained by adjoining a constant character to a [2,0] CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago.Arpit DasChethan N. GowdigereJagannath SantaraSpringerOpenarticleConformal and W SymmetryConformal Field TheoryNuclear and particle physics. Atomic energy. RadioactivityQC770-798ENJournal of High Energy Physics, Vol 2021, Iss 11, Pp 1-41 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Conformal and W Symmetry Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Conformal and W Symmetry Conformal Field Theory Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Arpit Das Chethan N. Gowdigere Jagannath Santara Classifying three-character RCFTs with Wronskian index equalling 0 or 2
description	Abstract In the modular linear differential equation (MLDE) approach to classifying rational conformal field theories (RCFTs) both the MLDE and the RCFT are identified by a pair of non-negative integers [n,l]. n is the number of characters of the RCFT as well as the order of the MLDE that the characters solve and l, the Wronskian index, is associated to the structure of the zeroes of the Wronskian of the characters. In this paper, we study [3,0] and [3,2] MLDEs in order to classify the corresponding CFTs. We reduce the problem to a “finite” problem: to classify CFTs with central charge 0 < c ≤ 96, we need to perform 6, 720 computations for the former and 20, 160 for the latter. Each computation involves (i) first finding a simultaneous solution to a pair of Diophantine equations and (ii) computing Fourier coefficients to a high order and checking for positivity. In the [3,0] case, for 0 < c ≤ 96, we obtain many character-like solutions: two infinite classes and a discrete set of 303. After accounting for various categories of known solutions, including Virasoro minimal models, WZW CFTs, Franc-Mason vertex operator algebras and Gaberdiel-Hampapura-Mukhi novel coset CFTs, we seem to have seven hitherto unknown character-like solutions which could potentially give new CFTs. We also classify [3,2] CFTs for 0 < c ≤ 96: each CFT in this case is obtained by adjoining a constant character to a [2,0] CFT, whose classification was achieved by Mathur-Mukhi-Sen three decades ago.
format	article
author	Arpit Das Chethan N. Gowdigere Jagannath Santara
author_facet	Arpit Das Chethan N. Gowdigere Jagannath Santara
author_sort	Arpit Das
title	Classifying three-character RCFTs with Wronskian index equalling 0 or 2
title_short	Classifying three-character RCFTs with Wronskian index equalling 0 or 2
title_full	Classifying three-character RCFTs with Wronskian index equalling 0 or 2
title_fullStr	Classifying three-character RCFTs with Wronskian index equalling 0 or 2
title_full_unstemmed	Classifying three-character RCFTs with Wronskian index equalling 0 or 2
title_sort	classifying three-character rcfts with wronskian index equalling 0 or 2
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/b35b856ff6114ab985e641c8ceaa7bba
work_keys_str_mv	AT arpitdas classifyingthreecharacterrcftswithwronskianindexequalling0or2 AT chethanngowdigere classifyingthreecharacterrcftswithwronskianindexequalling0or2 AT jagannathsantara classifyingthreecharacterrcftswithwronskianindexequalling0or2
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Classifying three-character RCFTs with Wronskian index equalling 0 or 2

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