Bootstrapping Fermionic Rational CFTs with Three Characters

Bae, Jin-Beom; Duan, Zhihao; Lee, Kimyeong; Lee, Sungjay; Sarkis, Matthieu

doi:10.48550/arxiv.2108.01647

Cited by 2 publications

(6 citation statements)

References 36 publications

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“…The first paper [41] appeared while the first version of our paper was being prepared. The second paper [42] appeared very soon after the first version of our paper and before the present second version of our paper. There is an overlap of our [3,0] results with (small) parts of both these papers but the methods seem to be quite different.…”

Section: Discussionmentioning

confidence: 76%

“…The MLDE approach to RCFTs has been covered in both the physics [14,15,[21][22][23][24][25][26][27][40][41][42] and the maths literature [28][29][30][31][32][33][34][35][36]. A status report on the program can be found in [19].…”

Section: Introductionmentioning

confidence: 99%

“…A status report on the program can be found in [19]. An extension of this program that includes fermionic RCFTs and up to three characters can be found in [27,42].…”

Section: Introductionmentioning

confidence: 99%

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Classifying three-character RCFTs with Wronskian Index equalling $\mathbf{0}$ or $\mathbf{2}$

Das,

Gowdigere,

Santara

2021

Preprint

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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.

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Section: Discussionmentioning

confidence: 76%

Section: Introductionmentioning

confidence: 99%

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Classifying three-character RCFTs with Wronskian Index equalling $\mathbf{0}$ or $\mathbf{2}$

Das,

Gowdigere,

Santara

2021

Preprint

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show abstract

“…In a previous paper on the subject, for the [3, 0] MLDE, the authors had obtained the analog of the formula (29) which was c = N 70 . Then, in a search for solutions with 0 < c ≤ 96, one only needs to perform 6720 computations and all of them were done.…”

Section: Solutions To the [3 3] Mldementioning

confidence: 99%

“…It should be noted that this is a two-parameter MLDE (both parameters are rigid) and is technically harder. But all it's admissible character solutions were obtained decades later in [27][28][29]. (see also [26,49]).…”

Section: Introductionmentioning

confidence: 99%

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

Das

Gowdigere

Santara

2021

J. High Energ. Phys.

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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.

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Bootstrapping Fermionic Rational CFTs with Three Characters

Cited by 2 publications

References 36 publications

Classifying three-character RCFTs with Wronskian Index equalling $\mathbf{0}$ or $\mathbf{2}$

Classifying three-character RCFTs with Wronskian Index equalling $\mathbf{0}$ or $\mathbf{2}$

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

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