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

(92 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 2 more Smart Citations

Modular properties of characters of the W3 algebra

Iles

Watts

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

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

confidence: 76%

Section: Jhep01(2016)089mentioning

confidence: 99%

See 1 more Smart Citation

Modular properties of characters of the W3 algebra

Iles

Watts

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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

show abstract

“…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.

View full text Add to dashboard Cite

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.

show abstract

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

Contact Info

Product

Resources

About

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

Contact Info

Product

Resources

About

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