Meromorphic Cosets and the Classification of Three-Character CFT

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

doi:10.48550/arxiv.2212.03136

Cited by 1 publication

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“…The recent work [50] proves, starting from the MLDE, that every Frobenius solution of the [2,6] study based on modular data and SL(2, Z) representation theory while the latter two directly solve the two-parameter MLDE. The stage (III) of the analysis that identifies genuine CFT amongst the large number (303, excluding an infinite class) of admissible character solutions was done in [30]. This again involved the application of the theory of meromorphic cosets [17].…”

Section: Introductionmentioning

confidence: 99%

“…This again involved the application of the theory of meromorphic cosets [17]. The final classification of [3,0] RCFT was presented in [30]. The [3,2] MLDE is also a two-parameter MLDE (both parameters rigid) and a classification of all it's admissible character solutions and that of CFT was given in [28].…”

Section: Introductionmentioning

confidence: 99%

“…We do some preliminary work in this direction. Given that the theory of meromorphic cosets [17] played a crucial role in the stage (III) analysis in earlier chapters of the MMS program ( [17] for [2,2] and [30] for [3,0]), we identify pairs of [3,3] admissible character solutions which form cosetbilinear relations 3.4. We find coset-bilinear relations involving meromorphic CFTs with central charges up to 64.…”

Section: Introductionmentioning

confidence: 99%

“…Step I: We solve the two Diophantine equations ( 27) and (30) simultaneously. We fix a value of N and and then obtain solutions to (27).…”

mentioning

confidence: 99%

“…Each such solution is a set of non-negative integers for N , m 1 , m 2 and m 3 . We take the m 1 , m 2 and N values of each such solution and see if we can find non-negative integer values for k that satisfy (30). At the end of this procedure, we will have a set of five non-negative integers, for N , m 1 , m 2 , m 3 and k which simultaneously solve (27) and (30).…”

mentioning

confidence: 99%

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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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