Note on W3 realizations of the bosonic string

Bastianelli, Fiorenzo; Ohta, Nobuyoshi

doi:10.1016/0370-2693(95)00192-n

Cited by 7 publications

(15 citation statements)

References 18 publications

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“…There should be no confusion from the fact that the (r, s) and (β, γ) fields have different conformal spins in different BRST operators. It is easy to verify that the (r, s) terms in {Q 1 , β}, for Q 1 given in (12), realise the Virasoro algebra with central charge c = 28.…”

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

“…In fact, we shall show that the BRST operator given in (10) provides an embedding of the Virasoro string into the non-critical W 3 string. As we shall see later, the BRST operators given in (11), (12) and (10) can all be re-expressed, by local similarity transformations, in the form…”

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

“…In the above similarity transformations, the most difficult part is the transformation of the BRST operators (11), (12) and (10) into the form given in (13). We shall discuss this procedure case by case.…”

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

“…where Q ′ 1 is Q 1 in Eqn. (12) with the γr term removed. The computation can be simplified by noting that the classical terms in R n also have degree zero under the (b 1 , c 1 ) and (β, γ) number operators.…”

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

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Embedding of the bosonic string into the W3 string

et al. 1995

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We investigate new realisations of the W 3 algebra with arbitrary central charge, making use of the fact that this algebra can be linearised by the inclusion of a spin-1 current. We use the new realisations with c = 102 and c = 100 to build non-critical and critical W 3 BRST operators. Both of these can be converted by local canonical transformations into a BRST operator for the Virasoro string with c = 28 − 2, together with a Kugo-Ojima topological term. Consequently, these realisations provide embeddings of the Virasoro string into non-critical and critical W 3 strings.

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Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

Section: The Non-critical W Brst Operator and Its Cohomologymentioning

confidence: 99%

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Embedding of the bosonic string into the W3 string

et al. 1995

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“…The BRST operator for W lin 3 was constructed in [8], it is nilpotent at c = 18 and, accordingly, c m = 27. On the other hand, as noted in the same paper [8], the nilpotency condition for the BRST charge operator for W (2) 3 [21] requires c (T T ) = 50. But this is just the value that arises upon substitution, into c T T in (4.12), of c = 18 which simultaneously produces the critical value for the central charge c m .…”

mentioning

confidence: 99%

Non-linear realizations of superconformal and W-algebras as embeddings of strings

Bellucci

Gribanov²,

Ivanov³

et al. 1998

Nuclear Physics B

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We propose a simple method for constructing representations of (super)conformal and nonlinear W -type algebras in terms of their subalgebras and corresponding Nambu-Goldstone fields. We apply it to N = 2 and N = 1 superconformal algebras and describe in this way various embeddings of strings and superstrings for which these algebras and their subalgebras define world-sheet symmetries. Besides reproducing the known examples, we present some new ones, in particular an embedding of the bosonic string with additional U(1) affine symmetry into N = 2 superstring. We also apply our method to the nonlinear W (2) 3algebra and demonstrate that the linearization procedure worked out for it some time ago gets a natural interpretation as a kind of string embedding. All these embeddings include the critical ones as particular cases. *

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Spinor field realizations of the half-integer strings

et al. 2009

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The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer W 2,s strings, where the BRST charge is written as Q B = Q 0 + Q 1 . Using this method, we reconstruct the nilpotent BRST charges Q 0 for the integer W 2,s strings and the half-integer W 2,s strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the half-integer W 2,s strings for the cases of s = 3/2, 5/2, and 7/2. Contents1. Introduction 1 2. Review of the grading BRST method 2 3. Construct BRST charges Q 0 for the integer and the half-integer W 2,s strings 4 3.1 Solutions for the case s = integer 5 3.2 Solutions for the case s = half-integer 6 4. Spinor field realizations of the half-integer W 2,s strings 8 4.1 Spinor field realizations of the W 2,3/2 string 8 4.2 Spinor field realizations of the W 2,5/2 string 8 4.3 Spinor field realizations of the W 2,7/2 string 10 5. Conclusion 11were obtained [24,25,26,27]. Recently, we constructed the nilpotent BRST charges of the spinor non-critical W 2,s (s=3,4) strings by taking account of the property of spinor field [28]. It was shown that certain integer W 2,s (s=3,4) algebras can be linearized as the W 1,2,s algebras by the inclusion of a spin-1 current. This provides a way of obtaining new realizations of the integer W 2,s strings. Based on the linear W 1,2,s algebras, the ghost field realizations and the spinor realizations of the spinor non-critical W 2,s strings were given in Refs. [29,30]. The half-integer W 2,s algebra with s = 3/2 is known as the N = 1 superconformal algebra or SW (3/2, 2) superconformal algebra. Recently, several constructions of the algebra were obtained in Refs. [31,32] . Much research had been done also on N = 2 superconformal algebra, in which another s = 3/2 current is added [33,34,35,36]. Correspondingly, the N = 1 and N = 2 superstrings had been investigated in [37,38]. In addition, the case of s = 5/2 was investigated in Ref. [39]. It was found that this algebra can not be closed with spin-2 current T and spin-5/2 current G only, and so there is no realization for this algebra. But by introducing other spin currents, this algebra may be linearized [40], which implies that the realizations of the algebra could be found. The W 2,s (s = 7/2, 9/2, 11/2, 13/2, 15/2) algebras were also studied in Ref. [41], in which the values of central charges for these algebras were given.Since up to now there is no work focused on the research of spinor field realizations of the half-integer W 2,s strings, we will construct the nilpotent BRST charges of spinor halfinteger W 2,s strings for the first time by using the grading BRST method. This method provides a more easy way to construct W 2,s algebras and strings. And the physical states can be obtained by the grading form of BRST operators for these strings. Firstly, we reconstruct the BRST charges Q 0 for integer W 2,s strings and the half-integer W 2,s strings. For each case we obtain four solutions. All these solutions indicate that we can construct the BRST...

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Note on W3 realizations of the bosonic string

Cited by 7 publications

References 18 publications

Embedding of the bosonic string into the W3 string

Embedding of the bosonic string into the W3 string

Non-linear realizations of superconformal and W-algebras as embeddings of strings

Spinor field realizations of the half-integer strings

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