Wn(2) algebras

B. L. Feigin; A. M. Semikhatov

doi:10.1016/j.nuclphysb.2004.06.056

W_n⁽²⁾ algebras

B. L. Feigin
, A. M. Semikhatov^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

63 Scopus citations

Abstract

We construct W-algebra generalizations of the sℓ̂(2) algebra - W algebras W_n⁽²⁾ generated by two currents E and F with the highest pole of order n in their OPE. The n = 3 term in this series is the Bershadsky-Polyakov W₃⁽²⁾ algebra. We define these algebras as a centralizer (commutant) of the U_qsℓ(n|1) quantum supergroup and explicitly find the generators in a factored, "Miura-like" form. Another construction of the W_n⁽²⁾ algebras is in terms of the coset sℓ̂(n|1)/sℓ̂(n). The relation between the two constructions involves the "duality" (k + n -1) (k′ + n - 1) = 1 between levels k and k′ of two sℓ̂(n) algebras.

Original language	English
Pages (from-to)	409-449
Number of pages	41
Journal	Nuclear Physics B
Volume	698
Issue number	3
DOIs	https://doi.org/10.1016/j.nuclphysb.2004.06.056
State	Published - 25 Oct 2004
Externally published	Yes

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title = "Wn(2) algebras",

abstract = "We construct W-algebra generalizations of the s{\^ℓ}(2) algebra - W algebras Wn(2) generated by two currents E and F with the highest pole of order n in their OPE. The n = 3 term in this series is the Bershadsky-Polyakov W3(2) algebra. We define these algebras as a centralizer (commutant) of the Uqsℓ(n|1) quantum supergroup and explicitly find the generators in a factored, {"}Miura-like{"} form. Another construction of the Wn(2) algebras is in terms of the coset s{\^ℓ}(n|1)/s{\^ℓ}(n). The relation between the two constructions involves the {"}duality{"} (k + n -1) (k′ + n - 1) = 1 between levels k and k′ of two s{\^ℓ}(n) algebras.",

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AU - Feigin, B. L.

AU - Semikhatov, A. M.

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N2 - We construct W-algebra generalizations of the sℓ̂(2) algebra - W algebras Wn(2) generated by two currents E and F with the highest pole of order n in their OPE. The n = 3 term in this series is the Bershadsky-Polyakov W3(2) algebra. We define these algebras as a centralizer (commutant) of the Uqsℓ(n|1) quantum supergroup and explicitly find the generators in a factored, "Miura-like" form. Another construction of the Wn(2) algebras is in terms of the coset sℓ̂(n|1)/sℓ̂(n). The relation between the two constructions involves the "duality" (k + n -1) (k′ + n - 1) = 1 between levels k and k′ of two sℓ̂(n) algebras.

AB - We construct W-algebra generalizations of the sℓ̂(2) algebra - W algebras Wn(2) generated by two currents E and F with the highest pole of order n in their OPE. The n = 3 term in this series is the Bershadsky-Polyakov W3(2) algebra. We define these algebras as a centralizer (commutant) of the Uqsℓ(n|1) quantum supergroup and explicitly find the generators in a factored, "Miura-like" form. Another construction of the Wn(2) algebras is in terms of the coset sℓ̂(n|1)/sℓ̂(n). The relation between the two constructions involves the "duality" (k + n -1) (k′ + n - 1) = 1 between levels k and k′ of two sℓ̂(n) algebras.

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W_n⁽²⁾ algebras

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