<i>W</i>algebra in the SU(3) parafermion model

Ding, Xiang-Mao; Fan, Heng; Shi, Kangjie; Wang, Pei; Zhu, Chang-Yu

doi:10.1103/physrevlett.70.2228

Cited by 11 publications

(20 citation statements)

References 24 publications

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“…Gepner proposed a parafermion algebra associated with any given untwisted affine Lie algebra G (1) [13,14], which has been subsequently used in the study of D-branes. The operator product expansions (OPEs) and the corresponding Z-algebra of the untwisted parafermions were studied in [15], and a W 3 -algebra was constructed from the SU(3) k parafermions. In [16] a W 5 -algebra was constructed by using the SU(2) k parafermions.…”

Section: Introductionmentioning

confidence: 99%

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A(2)2 parafermions: a new conformal field theory

2002

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A new parafermionic algebra associated with the homogeneous space A(2) 2 /U (1) and its corresponding Z-algebra have been recently proposed. In this paper, we give a free boson representation of the A (2) 2 parafermion algebra in terms of seven free fields. Free field realizations of the parafermionic energy-momentum tensor and screening currents are also obtained. A new algebraic structure is discovered, which contains a W -algebra type primary field with spin two. *

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Section: Introductionmentioning

confidence: 99%

“…For every field in the parafermion theory there are a pair of charges (λ, λ), which take values in the weight lattice. We denote such a field by φ λ, λ(z, z) [1,13,15]. Let H λ, λ be the subspace of H with the indicated charges.…”

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A(2)2 parafermions: a new conformal field theory

2002

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“…So, explicit expression of rational quantum currents in the coset space SU(2)/U(1) is not known yet. In the classical case, the currents defined on the coset space SU(2)/U(1) subject to a SU(2) nonlocal currents algebra, which is also referred to as parafermion algebra [23,24].…”

Section: Introductionmentioning

confidence: 99%

Quantum Currents in the Coset Space SU(2)/U(1)

Ding

Hou

Zhao

2002

Commun. Theor. Phys.

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We propose a rational quantum deformed nonlocal currents in the homogenous space SU (2) k /U (1), and in terms of it and a free boson field a representation for the Drinfeld currents of Yangian double at a general level k = c is obtained. In the classical limith → 0, the quantum nonlocal currents become SU (2) k parafermion, and the realization of Yangian double becomes the parafermion realization of SU (2) k current algebra.

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“…Gepner proposed a parafermion algebra associated with any given untwisted affine Lie algebra G (1) [18,19], which has been subsequently used in the study of D-branes. The operator product expansions (OPEs) and the corresponding Z-algebra of the untwisted parafermions were studied in [20,21].In this paper, we find a new type of nonlocal currents (quasi-particles), which will be referred to as twisted parafermions. The system contains a bosonic spin-1 field and six nonlocal fields with fractional spins.…”

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Twisted parafermions

Ding¹,

Gould²,

Zhang³

2002

Physics Letters B

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A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2) 2 is given. 11.25.Hf; 03.65.Fd; 11.10.Lm.The introduction of the Z k parafermions [1] in the context of statistical models and conformal field theory [2] is perhaps one of the most significant conceptual advances in modern theoretical physics. From field theory point of view, parafermions generalize the Majorano fermions and have found important applications in superstring theory [3,4], fractional supersymmetry and fractional superstring [5], T -duality [6] and mirror symmetry [7]. In a very recent work by Maldacena, Moore and Seiberg, D-branes were constructed with the help of the Z k parafermions [8]. From statistical physics point of view, parafermions are related to the exclusion statistics introduced by Haldane [9]. In particular, the Z k parafermion models offer various extensions of the Ising model which corresponds to the k = 2 case [1]. Other examples include the 3-state Potts model (k = 3) [1,10] and the Ashkin-Teller model (k = 4) [11]. Parafermions also have applications in Quantum Hall Effects [12], Bose-Einstein Condensates [13] and Quantum Computations [14].The category for parafermions (nonlocal operators) is the generalized vertex operator algebra [15,16]. The Z k parafermion algebra was referred to as Z-algebra in [15,16], and the Z k parafermions are canonically modified Zalgebras acting on certain quotient spaces A(1) 1 -modules defined by the action of an infinite cyclic group. It was proved that the Z-algebra is identical with the A (1) 1 parafermion. The Z k parafermion characters and their singular vectors were studied in [17].The imoprtance of parafermions inspired many researchers to study various extensions of the Z k parafermions which are basically related to the simplest A (1) 1 algebra. Gepner proposed a parafermion algebra associated with any given untwisted affine Lie algebra G (1) [18,19], which has been subsequently used in the study of D-branes. The operator product expansions (OPEs) and the corresponding Z-algebra of the untwisted parafermions were studied in [20,21].In this paper, we find a new type of nonlocal currents (quasi-particles), which will be referred to as twisted parafermions. The system contains a bosonic spin-1 field and six nonlocal fields with fractional spins. Some of the fields are in the Ramond sector and some are in the Neveu-Schwarz (NS) sector. They correspond to a new type of qusi-particles or generalized Majorana fermions. We derive the corresponding twisted Z-algebra and the Jacobi-type identities for the twisted parafermion currents. From the twisted parafermions, we construct a new conformal field th...

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Walgebra in the SU(3) parafermion model

Cited by 11 publications

References 24 publications

A(2)2 parafermions: a new conformal field theory

A(2)2 parafermions: a new conformal field theory

Quantum Currents in the Coset Space SU(2)/U(1)

Twisted parafermions

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