W3 strings, parafermions and the Ising model

Freeman, Michael; West, Peter

doi:10.1016/0370-2693(93)91243-g

Cited by 7 publications

(14 citation statements)

References 18 publications

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“…where ρ and the parameters α 0 , α ± are as before (see (14)), and w is an element of the su(4) Weyl group W while σ can be an element of the su(4) affine Weyl groupŴ . The ghost number at which the state with momentum (61) occurs is given by −l w (σ), where l w (σ) is the twisted length of σ…”

Section: The Complete Cohomologymentioning

confidence: 99%

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BRST cohomology of the critical W string

Boonstra

1994

Class. Quantum Grav.

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We study the cohomology of the critical W 4 string using the W 4 BRST charge in a special basis in which it contains three separately nilpotent BRST charges. This allows us to obtain the physical operators in three steps. In the first step we obtain the cohomology associated to a spin-four constraint only, and it contains operators of the c = 4 5 W 3 minimal model. In the next step, where the spin-three constraint is added, these operators get dressed to operators of the c = 10Virasoro minimal model. Finally, the Virasoro constraint is added to obtain the cohomology of the critical W 4 string. We describe the structure of the complete cohomology and compare with other results.

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Section: The Complete Cohomologymentioning

confidence: 99%

“…This relation is clarified by going to a new basis of fields introduced in [10]. In this new basis, a special subsector of the W 3 model was seen to correspond to the Ising model [11], see also [12,10,13,14].…”

Section: Introductionmentioning

confidence: 99%

BRST cohomology of the critical W string

Boonstra

1994

Class. Quantum Grav.

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“…It was recently shown that the Ising model that arises provides a two-scalar realization of the c = 1/2 parafermion theory corresponding to the coset SU (2) 2 /U (1) [2]. A consequence of this fact is that the W 3 string has embedded within it a non-linear W algebra containing an infinite number of generators W s , one for each spin s = 2, .…”

mentioning

confidence: 99%

“…We argue that this connection between parafermions and W strings can be generalised, and give evidence that the BRST charge for the W N string has a natural decomposition [5,2,6] of the form Q(W N ) = Q 0 + Q 1 , where Q 1 is just the second of the two screening charges discussed above, evaluated for k = N − 1. We conjecture further that, using the series of cosets SU (N − r + 1) r /SU (N − r) r × U (1), Q(W N ) has a decomposition [5,2,6] of the form Q 1 is a screening charge for the above coset constructed from the 2(N − r) bosonic fields that are used to describe this coset in the Wakimoto realization [7].…”

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Parafermions, W strings and their BRST charges

Freeman

West

1994

Physics Letters B

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We show how to relate the parafermions that occur in the W 3 string to the standard construction of parafermions. This result is then used to show that one of the screening charges that occurs in parafermionic theories is precisely the non-trivial part of the W 3 string BRST charge. A way of generalizing this pattern for a W N string is explained. This enables us to construct the full BRST charge for a W 2,N string and to prove the relation of such a string to the algebra W N−1 for arbitrary N , We also show how to calculate part of the BRST charge for a W N string, and we explain how our method might be extended to obtain the full BRST charge for such a string.

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On realizing the bosonic string as a noncritical W3-string

Bergshoeff¹,

Boonstra²,

Roo³

1995

Physics Letters B

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We discuss a realization of the bosonic string as a noncritical W 3 -string. The relevant noncritical W 3 -string is characterized by a Liouville sector which is restricted to a (non-unitary) (3, 2) W 3 minimal model with central charge contribution c l = −2. Furthermore, the matter sector of this W 3 -string contains 26 free scalars which realize a critical bosonic string. The BRST operator for this W 3 -string can be written as the sum of two, mutually anticommuting, nilpotent BRST operators: Q = Q 0 + Q 1 in such a way that the scalars which realize the bosonic string appear only in Q 0 while the central charge contribution of the fields present in Q 1 equals zero. We argue that, in the simplest case that the Liouville sector is given by the identity operator only, the Q 1 -cohomology is given by a particular (non-unitary) (3, 2) Virasoro minimal model at c = 0.

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W3 strings, parafermions and the Ising model

Cited by 7 publications

References 18 publications

BRST cohomology of the critical W string

BRST cohomology of the critical W string

Parafermions, W strings and their BRST charges

On realizing the bosonic string as a noncritical W3-string

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