The W N Minimal Model Classification

Beltaos, Elaine; Gannon, Terry

doi:10.1007/s00220-012-1473-4

Cited by 7 publications

(8 citation statements)

References 31 publications

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“…To take a concrete series WM (3, 3p + 1) has central charge In these models there is also a minimum value of h which is less than 0, which is 9) and so again the leading term from (4.10) comes from the (β/πi)(cE 4 )/1440 term and is in agreement with the analysis from the Verma module, (6.3). This is perhaps not obvious, since for any particular non-unitary minimal model, a representation will have an infinite number of terms in its composition series, and this could in principle change the τ → +i∞ behaviour.…”

Section: The C → −∞ Limit: Non-unitary Minimal Modelssupporting

confidence: 76%

“…We have checked that the formulae agree numerically, using the W 3 Smatrices which can be found in [9]. Next, we assumed that the equations take the form given in (4.15) and (4.16) but with an unspecified S-matrix and fitted the values of the S-matrix using various different values of τ , recovering the correct S-matrix.…”

Section: Jhep01(2016)089mentioning

confidence: 99%

“…The possible modular invariant partition functions for minimal models have been classified by Beltaos and Gannon in [9]. We are not interested in the particular partition functions, but just the representations that arise, and so we shall simply call these WM (p, p ′ ), for convenience.…”

Section: Jhep01(2016)089mentioning

confidence: 99%

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Modular properties of characters of the W3 algebra

Iles

Watts

2016

J. High Energ. Phys.

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In a previous work, exact formulae and differential equations were found for traces of powers of the zero mode in the W 3 algebra. In this paper we investigate their modular properties, in particular we find the exact result for the modular transformations of traces of W n 0 for n = 1, 2, 3, solving exactly the problem studied approximately by Gaberdiel, Hartman and Jin. We also find modular differential equations satisfied by traces with a single W 0 inserted, and relate them to differential equations studied by Mathur et al. We find that, remarkably, these all seem to be related to weight 0 modular forms with expansions with non-negative integer coefficients.

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Section: The C → −∞ Limit: Non-unitary Minimal Modelssupporting

confidence: 76%

Section: Jhep01(2016)089mentioning

confidence: 99%

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Modular properties of characters of the W3 algebra

Iles

Watts

2016

J. High Energ. Phys.

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“…For any coset CFT, it is a hard problem to classify all modular-invariant partition functions [8,9]. Modular invariants of a coset CFT are intimately related to modular invariants of WZW models.…”

mentioning

confidence: 99%

Conformal embeddings and higher-spin bulk duals

Kumar

Sharma

2017

Phys. Rev. D

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It is well-known that conformal embeddings can be used to construct non-diagonal modular invariants for affine lie algebras. This idea can be extended to construct infinite series of non-diagonal modular invariants for coset CFTs. In this paper, we systematically approach the problem of identifying higher-spin bulk duals for these kind of non-diagonal invariants. In particular, for a special value of the 't Hooft coupling, there exist a class of partition functions that have enhanced supersymmetry, which should be reflected in a bulk dual. As a illustration of this, we show that a partition function of a orthogonal group coset CFT has a $\mathcal N=1$ supersymmetric higher-spin bulk dual, in the 't Hooft limit. We also propose that two of the series of CFT partition functions, obtained from conformal embeddings, are equal, generalising the well-known dual interpretation of the 3-state Potts model as a $\frac{SU(2)_3 \otimes SU(2)_1}{SU(2)_4}$ and also as a $\frac{SU(3)_1 \otimes SU(3)_1}{SU(3)_2}$ coset model.Comment: 40 pages, 1 figure, Version to appear in Physical Review

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“…We are concerned with the simplest W3 minimal models, i.e. those with diagonal modular invariant[22].…”

mentioning

confidence: 99%

The fully packed loop model as a non-rationalW₃conformal field theory

Dupic¹,

Estienne²,

Ikhlef³

2016

J. Phys. A: Math. Theor.

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The fully packed loop (FPL) model is a statistical model related to the integrable U q ( sl 3 ) vertex model. In this paper we study the continuum limit of the FPL. With the appropriate weight of non-contractible loops, we give evidence of an extended W 3 symmetry in the continuum. The partition function on the torus is calculated exactly, yielding new modular invariants of W 3 characters. The full CFT spectrum is obtained, and is found to be in excellent agreement with exact diagonalisation.

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The W N Minimal Model Classification

Cited by 7 publications

References 31 publications

Modular properties of characters of the W3 algebra

Modular properties of characters of the W3 algebra

Conformal embeddings and higher-spin bulk duals

The fully packed loop model as a non-rationalW₃conformal field theory

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The W N Minimal Model Classification

Cited by 7 publications

References 31 publications

Modular properties of characters of the W3 algebra

Modular properties of characters of the W3 algebra

Conformal embeddings and higher-spin bulk duals

The fully packed loop model as a non-rationalW3conformal field theory

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Product

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The fully packed loop model as a non-rationalW₃conformal field theory