and as Vertex Operator Extensions¶of Dual Affine Algebras

Bowcock, P.; Feigin, Boris; Semikhatov, A. M.; Taormina, Anne

doi:10.1007/pl00005536

Cited by 33 publications

(38 citation statements)

References 32 publications

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“…The ;θ notation is for the spectral flow transform, see (B.5) [13,33]. The four different sectors (Ramond, Neveu-Schwarz, super-Ramond, and super-Neveu-Schwarz) are mapped under the S and T transformations as indicated in (B.35).…”

Section: Formulation Of the Main Resultmentioning

confidence: 99%

“…Admissible sℓ(2|1) representations L r,s,ℓ,u;θ . The admissible sℓ(2|1)-representations, which belong to the class of irreducible highest-weight representations characterized by the property that the corresponding Verma modules are maximal elements with respect to the (appropriately defined) Bruhat order, have arisen in a vertex-operator extension of two sℓ(2) algebras with the "dual" levels k and k ′ such that (k + 1)(k ′ + 1) = 1 [33]; via this extension sℓ(2) k ⊕ sℓ(2) k ′ → sℓ(2|1) k , the admissible sℓ(2|1) representations are related to the admissible sℓ(2) representations [45]. We fix the sℓ(2|1) level as k = ℓ u − 1 with coprime positive integers ℓ and u.…”

Section: Discussionmentioning

confidence: 99%

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Higher-Level Appell Functions, Modular Transformations, and Characters

Semikhatov

Taorimina

Tipunin

2005

Commun. Math. Phys.

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Bore Fe ginu po sluqa ego p tides tileti ABSTRACT. We study modular transformation properties of a class of indefinite theta series involved in characters of infinite-dimensional Lie superalgebras. The level-ℓ Appell functions K ℓ satisfy open quasiperiodicity relations with additive theta-function terms emerging in translating by the "period." Generalizing the well-known interpretation of theta functions as sections of line bundles, the K ℓ function enters the construction of a section of a rank-(ℓ + 1) bundle V ℓ,τ . We evaluate modular transformations of the K ℓ functions and construct the action of an SL(2, Z) subgroup that leaves the section of V ℓ,τ constructed from K ℓ invariant.Modular transformation properties of K ℓ are applied to the affine Lie superalgebra sℓ(2|1) at rational level k > −1 and to the N = 2 super-Virasoro algebra, to derive modular transformations of "admissible" characters, which are not periodic under the spectral flow and cannot therefore be rationally expressed through theta functions. This gives an example where constructing a modular group action involves extensions among representations in a nonrational conformal model.

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Section: Formulation Of the Main Resultmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Higher-Level Appell Functions, Modular Transformations, and Characters

Semikhatov

Taorimina

Tipunin

2005

Commun. Math. Phys.

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“…Since these states generate relaxed highest-weight modules in which the charged singular vector generates exactly the identity module, their irreducible module 13 χ R ⋆ µ1,µ2;θ (z, q) will not 12 There is a minor difference in the picture provided in [3], as the L 0 direction is inverted in that paper. 13 Here we really consider the irreducible modules R ⋆ from which the charged singular vector has been factored out.…”

Section: The I 0 Charactermentioning

confidence: 99%

Logarithmic lift of the model

et al. 2004

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This paper carries on the investigation of the non-unitary su(2) −1/2 WZW model. An essential tool in our first work on this topic was a free-field representation, based on a c = −2 ηξ ghost system, and a Lorentzian boson. It turns out that there are several 'versions' of the ηξ system, allowing different su(2) −1/2 theories. This is explored here in details. In more technical terms, we consider extensions (in the c = −2 language) from the small to the large algebra representation and, in a further step, to the full symplectic fermion theory. In each case, the results are expressed in terms of su(2) −1/2 representations. At the first new layer (large algebra), continuous representations appear which are interpreted in terms of relaxed modules. At the second step (symplectic formulation), we recover a logarithmic theory with its characteristic signature, the occurrence of indecomposable representations. To determine whether any of these three versions of the su(2) −1/2 WZW is welldefined, one conventionally requires the construction of a modular invariant. This issue, however, is plagued with various difficulties, as we discuss.

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“…This "duality" between two levels, k and p − 1, was extensively used in [39,40] (see also the references therein); in particular,…”

Section: (57(4)mentioning

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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and as Vertex Operator Extensions¶of Dual Affine Algebras

Cited by 33 publications

References 32 publications

Higher-Level Appell Functions, Modular Transformations, and Characters

Higher-Level Appell Functions, Modular Transformations, and Characters

Logarithmic lift of the model

Virasoro Central Charges for Nichols Algebras

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