Parafermionic representation of the affine algebra at fractional level

Bowcock, P.; Hayes, M.; Taormina, Anne

doi:10.1016/s0370-2693(99)01251-4

Cited by 6 publications

(9 citation statements)

References 16 publications

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“…: c = − 6 Ψ + 3 (8.54) and we can see that central charge of the theory matches the previous two realizations. The emergence of the parafermion VOA from such a coset is less familiar than the previous constructions, but it known [41]. Essentially, the para-fermions are used to dress spin 1 2 modules for U(2) in order to assemble the odd currents of U(2|1).…”

Section: Jhep01(2019)160mentioning

confidence: 99%

Vertex algebras at the corner

Gaiotto

Rapčák

2019

J. High Energ. Phys.

129

321

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We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N = 4 Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of the four-dimensional gauge theory. The gauge theory construction equips the vertex algebras with collections of modules labelled by supersymmetric interface line defects. We discuss in detail the simplest class of algebras Y L,M,N , which generalizes W N algebras. We uncover tantalizing relations between Y L,M,N , the topological vertex and the W 1+∞ algebra.

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Section: Jhep01(2019)160mentioning

confidence: 99%

Vertex algebras at the corner

Gaiotto

Rapčák

2019

J. High Energ. Phys.

129

321

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“…The above argument is also strongly supported by the detailed knowledge we have of a class of irreducible representations of sℓ(2|1) at admissible level k 1 = 1 u − 1, u ∈ N + 1, and their corresponding characters. Their branching functions into characters of the subalgebra sℓ(2) k 1 were shown in [20,8] to involve characters of a rational torus A u(u−1) and of the parafermionic algebra Z u−1 . The latter can be obtained as the coset sℓ(2) u−1 / u(1), providing us with the dual sℓ(2) k 2 in the construction of sℓ(2|1) k 1 (note that one indeed has (1.1) with k 2 = u − 1).But there is an additional remarkable observation: the u(1) mixings involved in the above coset argument conspire so as to extend sℓ(2|1) k 1 ⊕ u(1) to the exceptional affine Lie superalgebra D(2|1; k 2 ) k 1 .…”

mentioning

confidence: 99%

and as Vertex Operator Extensions¶of Dual Affine Algebras

Bowcock¹,

Feigin²,

Semikhatov³

et al. 2000

Commun. Math. Phys.

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Abstract. We discover a realisation of the affine Lie superalgebra sℓ(2|1) and of the exceptional affine superalgebra D(2|1; α) as vertex operator extensions of two sℓ(2) algebras with 'dual ' levels (and an auxiliary level-1 sℓ(2) algebra). The duality relation between the levels is (k 1 +1)(k 2 +1) = 1. We construct the representation of sℓ(2|1) k1 on a sum of tensor products of sℓ(2) k1 , sℓ(2) k2 , and sℓ(2) 1 modules and decompose it into a direct sum over the sℓ(2|1) k1 spectral flow orbit. This decomposition gives rise to character identities, which we also derive. The extension of the construction to D(2|1; k 2 ) k1 is traced to the properties of sℓ(2) ⊕ sℓ(2) ⊕ sℓ(2) embeddings into D(2|1; α) and their relation with the dual sℓ(2) pairs. Conversely, we show how the sℓ(2) k2 representations are constructed from sℓ(2|1) k1 representations.

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“…As suggested by Gaiotto-Rapčák dualities [13] (see also [34]), the coset is conjecturally dual to the cigar model described by (1.1)…”

Section: Introductionmentioning

confidence: 75%

FZZ-triality and large $\mathcal{N}=4$ super Liouville theory

Creutzig,

Hikida

2021

Preprint

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We examine dualities of two dimensional conformal field theories by applying the methods developed in previous works. We first derive the duality between SL(2|1) k /(SL(2) k ⊗ U (1)) coset and Witten's cigar model or sine-Liouville theory. The latter two models are Fateev-Zamolodchikov-Zamolodchikov (FZZ-)dual to each other, hence the relation of the three models is named FZZ-triality. These results are used to study correlator correspondences between large N = 4 super Liouville theory and a coset of the form Y (k 1 , k 2 )/SL(2) k1+k2 , where Y (k 1 , k 2 ) consists of two SL(2|1) ki and free bosons or equivalently two U (1) cosets of D(2, 1; k i − 1) at level one. These correspondences are a main result of this paper. The FZZtriality acts as a seed of the correspondence, which in particular implies a hidden SL(2. We also construct boundary actions in sine-Liouville theory as another use of the FZZ-triality. Furthermore, we generalize the FZZ-triality to the case with SL(n|1) k /(SL(n) k ⊗ U (1)) for arbitrary n > 2.

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Parafermionic representation of the affine algebra at fractional level

Abstract: The four fermionic currents of the affine superalgebraŝl(2|1; C) at fractional level k = 1 u − 1, u ∈ N are shown to be realised in terms of a free scalar field, anŝl(2; C) doublet field and a primary field of the parafermionic algebra Z u−1 .

Cited by 6 publications

References 16 publications

Vertex algebras at the corner

Vertex algebras at the corner

and as Vertex Operator Extensions¶of Dual Affine Algebras

FZZ-triality and large $\mathcal{N}=4$ super Liouville theory

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