On the triplet vertex algebra <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi mathvariant="script">W</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>

Adamović, Dražen; Milas, Antun

doi:10.1016/j.aim.2007.11.012

Cited by 158 publications

(223 citation statements)

References 32 publications

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“…The modes of the W a combine with the Virasoro generators L n to form an extended chiral algebra [85]. In particular, the zero modes of the W 0,± generate a global SL(2) symmetry -not to be confused of the SL(2, C) global conformal group.…”

Section: Triplet Modelmentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is modelindependent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

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Section: Triplet Modelmentioning

confidence: 99%

The ABC (in any D) of logarithmic CFT

Hogervorst

Paulos

Vichi

2017

J. High Energ. Phys.

103

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“…Already a sample of new identities can be obtained from the triplet vertex algebra [5,6,7,8,9]. It is interesting that classification of modules for the triplet algebra can be reduced to a single constant term identity [5].…”

Section: • Various Calculations With Products Of Bosonic Vertex Operamentioning

confidence: 99%

“…We begin with a short review of the triplet algebra W(p), its orbifold subalgebras W(p) Γ , and status of classifications of their modules; more details can be found in [2,3,5].…”

Section: • Various Calculations With Products Of Bosonic Vertex Operamentioning

confidence: 99%

Vertex Algebras W(p)^Amand W(p)^Dmand Constant Term Identities

Adamović¹,

Lin²,

Milas³

2015

SIGMA

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Abstract. We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c = 1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p) Am ) and A(W(p) Dm ), where A m and D m are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p) Γ -modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun.

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“…But given a q i,i = −1 and trying to reconstruct a screening in general leads to the condition 3 Recall that rational conformal field theories are generally defined as the cohomology of a complex associated with the screenings, whereas logarithmic models are defined by the kernel (cf. [18,27,28,29]). In particular, this allows interesting logarithmic conformal models to exist in the cases where the rational model is nonexistent (the (p, 1) series) or trivial (the (2, 3) model).…”

Section: Points To Notementioning

confidence: 99%

Virasoro Central Charges for Nichols Algebras

Semikhatov

2014

Mathematical Lectures From Peking University

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ABSTRACT. A Virasoro central charge can be associated with each Nichols algebra with diagonal braiding in a way that is invariant under the Weyl groupoid action. The central charge takes very suggestive values for some items in Heckenberger's list of rank-2 Nichols algebras. In particular, this might be viewed as an indication of the existence of reasonable logarithmic extensions of W 3 ≡ WA 2 , WB 2 , and WG 2 models of conformal field theory. In the W 3 case, the construction of an octuplet extended algebra-a counterpart of the triplet (1, p) algebra-is outlined.

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On the triplet vertex algebra W(p)

Cited by 158 publications

References 32 publications

The ABC (in any D) of logarithmic CFT

The ABC (in any D) of logarithmic CFT

Vertex Algebras W(p)^Amand W(p)^Dmand Constant Term Identities

Virasoro Central Charges for Nichols Algebras

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On the triplet vertex algebra W(p)

Cited by 158 publications

References 32 publications

The ABC (in any D) of logarithmic CFT

The ABC (in any D) of logarithmic CFT

Vertex Algebras W(p)Amand W(p)Dmand Constant Term Identities

Virasoro Central Charges for Nichols Algebras

Contact Info

Product

Resources

About

Vertex Algebras W(p)^Amand W(p)^Dmand Constant Term Identities