Fusion rules in N=1 superconformal minimal models

Minces, Pablo; Namazie, M.A.; Núñez, Carmen

doi:10.1016/s0370-2693(98)00038-0

Cited by 5 publications

(2 citation statements)

References 15 publications

(35 reference statements)

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“…It is remarkable that when we assemble In each case, the number of super conformal primaries is an even number; half of them are Neveu-Schwarz fields and the other half are Ramond fields. Now, to compute how many conformal primary fields there are in the SM(m + 2, m) CFT, we need to know how a super conformal representation decomposes into conformal representations [39][40][41][42]. First we note how Neveu-Schwarz super conformal representations decompose:…”

Section: Jhep04(2021)294mentioning

confidence: 99%

Wronskian indices and rational conformal field theories

Das

Gowdigere

Santara

2021

J. High Energ. Phys.

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The classification scheme for rational conformal field theories, given by the Mathur-Mukhi-Sen (MMS) program, identifies a rational conformal field theory by two numbers: (n, l). n is the number of characters of the rational conformal field theory. The characters form linearly independent solutions to a modular linear differential equation (which is also labelled by (n, l)); the Wronskian index l is a non-negative integer associated to the structure of zeroes of the Wronskian.In this paper, we compute the (n, l) values for three classes of well-known CFTs viz. the WZW CFTs, the Virasoro minimal models and the $$ \mathcal{N} $$ N = 1 super-Virasoro minimal models. For the latter two, we obtain exact formulae for the Wronskian indices. For WZW CFTs, we get exact formulae for small ranks (upto 2) and all levels and for all ranks and small levels (upto 2) and for the rest we compute using a computer program. We find that any WZW CFT at level 1 has a vanishing Wronskian index as does the $$ {\hat{\mathbf{A}}}_{\mathbf{1}} $$ A ̂ 1 CFT at all levels. We find intriguing coincidences such as: (i) for the same level CFTs with $$ {\hat{\mathbf{A}}}_{\mathbf{2}} $$ A ̂ 2 and $$ {\hat{\mathbf{G}}}_{\mathbf{2}} $$ G ̂ 2 have the same (n, l) values, (ii) for the same level CFTs with $$ {\hat{\mathbf{B}}}_{\mathbf{r}} $$ B ̂ r and $$ {\hat{\mathbf{D}}}_{\mathbf{r}} $$ D ̂ r have the same (n, l) values for all r ≥ 5.Classifying all rational conformal field theories for a given (n, l) is one of the aims of the MMS program. We can use our computations to provide partial classifications. For the famous (2, 0) case, our partial classification turns out to be the full classification (achieved by MMS three decades ago). For the (3, 0) case, our partial classification includes two infinite series of CFTs as well as fifteen “discrete” CFTs; except three all others have Kac-Moody symmetry.

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Section: Jhep04(2021)294mentioning

confidence: 99%

Wronskian indices and rational conformal field theories

Das

Gowdigere

Santara

2021

J. High Energ. Phys.

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show abstract

“…In each case, the number of super conformal primaries is an even number; half of them are Neveu-Schwarz fields and the other half are Ramond fields. Now, to compute how many conformal primary fields there are in the SM(m + 2, m) CFT, we need to know how a super conformal representation decomposes into conformal representations [39], [40], [41], [42]. First we note how Neveu-Schwarz super conformal representations decompose:…”

Section: Minimal Model Cfts 41 Virasoro Minimal Modelsmentioning

confidence: 99%

Wronskian Indices and Rational Conformal Field Theories

Das,

Gowdigere,

Santara

2020

Preprint

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The classification scheme for rational conformal field theories, given by the Mathur-Mukhi-Sen (MMS) program, identifies a rational conformal field theory by two numbers: (n, l). n is the number of characters of the rational conformal field theory. The characters form linearly independent solutions to a modular linear differential equation (which is also labelled by (n, l)); the Wronskian index l is a non-negative integer associated to the structure of zeroes of the Wronskian.In this paper, we compute the (n, l) values for three classes of well-known CFTs viz. the WZW CFTs, the Virasoro minimal models and the N = 1 super-Virasoro minimal models. For the latter two, we obtain exact formulae for the Wronskian indices. For WZW CFTs, we get exact formulae for small ranks (upto 2) and all levels and for all ranks and small levels (upto 2) and for the rest we compute using a computer program. We find that any WZW CFT at level 1 has a vanishing Wronskian index as does the Â1 CFT at all levels. We find intriguing coincidences such as: (i) for the same level CFTs with Â2 and Ĝ2 have the same (n, l) values, (ii) for the same level CFTs with Br and Dr have the same (n, l) values for all r ≥ 5.Classifying all rational conformal field theories for a given (n, l) is one of the aims of the MMS program. We can use our computations to provide partial classifications. For the famous (2, 0) case, our partial classification turns out to be the full classification (achieved by MMS three decades ago). For the (3, 0) case, our partial classification includes two infinite series of CFTs as well as fifteen "discrete" CFTs; except three all others have Kac-Moody symmetry.

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Consistent superconformal boundary states

Nepomechie¹

2001

J. Phys. A: Math. Gen.

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We propose a supersymmetric generalization of Cardy's equation for consistent N = 1 superconformal boundary states. We solve this equation for the superconformal minimal models SM(p/p + 2) with p odd, and thereby provide a classification of the possible superconformal boundary conditions . In addition to the Neveu-Schwarz (N S) and Ramond (R) boundary states, there are N S states. The N S and N S boundary states are related by a Z 2 "spin-reversal" transformation. We treat the tricritical Ising model as an example, and in an appendix we discuss the (non-superconformal) case of the Ising model.

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Fusion rules in N=1 superconformal minimal models

Cited by 5 publications

References 15 publications

Wronskian indices and rational conformal field theories

Wronskian indices and rational conformal field theories

Wronskian Indices and Rational Conformal Field Theories

Consistent superconformal boundary states

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