Note on N = 0 String as N = 1 String

Ishikawa, Hirohisa; Kato, Mitsuhiro

doi:10.1142/s0217732394000538

Cited by 31 publications

(59 citation statements)

References 4 publications

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“…The quantum version of the canonical transformation here described has been also found in a recent paper by Ishikawa and Kato [7].…”

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confidence: 68%

A locally supersymmetric action for the bosonic string

Bastianelli

1994

Physics Letters B

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Recently Berkovits and Vafa have shown that the bosonic string can be viewed as the fermionic string propagating in a particular background. Such a background is described by a somewhat unusual N = 1 superconformal system. By coupling it to N = 1 supergravity I construct a local supersymmetric action for the bosonic string. † e-mail: fiorenzo@nbivax.nbi.dkIn a recent paper Berkovits and Vafa [1] have shown how to embed the bosonic string into the N = 1 superstring. After identifying a suitable N = 1 superconformal system which could be used as a background for the N = 1 string, they showed how the bosonic string amplitudes are reproduced by the fermionic string propagating on it. They also showed how to view the N = 1 string as the N = 2 string moving in a particular background, and were led to conjecture the existence of an "universal string theory" which contains all string theories as particular choices of the vacuum (see also ref.[2] for some interesting remarks on the search for an universal string theory). In this letter I analyze the structure of the N = 1 superconformal system used by Berkovits and Vafa to embed the bosonic string into the N = 1 string. I look at the classical limit of such a system and by coupling it to N = 1 supergravity I shall produce a locally supersymmetric action for the bosonic string. I will conclude presenting few comments on its quantization and on its relation to the usual bosonic string action.I start by recalling the Berkovits-Vafa superconformal system. It is realized on a matter system with stress tensor T m and central charge c = 26 plus an anticommuting bc-system (b 1 , c 1 ) of spin ( 3 2 , − 1 2 ). The generator of the N = 1 superconformal algebra areand their OPE generates a superconformal algebra with c = 15. For simplicity I will consider the matter system as given by the usual 26 free scalar fields X i , and omit showing the index i in the following. By dropping the improvement terms in (1), i.e. considering the generatorsand keeping only single contractions in their OPE, one obtains a classical superconformal algebra without central charges. Such a superconformal algebra, together with its rightmoving counterpart, describes the classical symmetries of the action1The supersymmetry transformation rules can be easily computed from the generators and read δX = ǫc 1 ∂X +ǭc 1∂ X,where∂ǫ = 0 and ∂ǭ = 0. This realization of supersymmetry is quite unusual. It looks spontaneously broken (δc 1 = ǫ + . . .) and it is non-linearly realized. For this last reason it is difficult to rewrite the model with superfields and couple it to supergravity using standard superspace techniques. However, one can follow another well-known path, that of using the Noether method to gauge global symmetries. This was in fact the strategy used in [3] to construct a locally supersymmetric action for the spinning string. I will now follow the same path for the Berkovits-Vafa supersymmetric model and obtain a locally supersymmetric action for the bosonic string. The coupling to gravity is straightf...

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“…The quantum version of the canonical transformation here described has been also found in a recent paper by Ishikawa and Kato [7].…”

supporting

confidence: 68%

A locally supersymmetric action for the bosonic string

Bastianelli

1994

Physics Letters B

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“…Anyway, along with the results on explicit evaluation of topological singular vectors in the sl(2) terms, this partial argument in favour of the one-to-one correspondence between the singular states strongly suggests that the sl(2) Kač-Moody algebra and the topological conformal algebra possess identical singular vectors (when c = 3, see the next section). Recall also that 'the same' ordinary matter theory enters our constructions for the topological algebra (section 2) and the sl (2) As noted above, it would be interesting to understand these relations not just between the singular states, but rather between the corresponding algebras, in the context of universal string theory [27,28,29].…”

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confidence: 98%

The MFF Singular Vectors in Topological Conformal Theories

Semikhatov

1994

Mod. Phys. Lett. A

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It is argued that singular vectors of the topological conformal (twisted N = 2) algebra are identical with singular vectors of the sl(2) Kač-Moody algebra. An arbitrary matter theory can be dressed by additional fields to make up a representation of either the sl(2) current algebra or the topological conformal algebra. The relation between the two constructions is equivalent to the Kazama-Suzuki realisation of a topological conformal theory as sl(2) ⊕ u(1)/u(1). The Malikov-Feigin-Fuchs (MFF) formula for the sl(2) singular vectors translates into a general expression for the topological singular vectors. The MFF/topological singular states are observed to vanish in Witten's free-field construction of the (twisted) N = 2 algebra, derived from the Landau-Ginzburg formalism.

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“…By adding fermionic gauge fields to the bosonic string, it was recently shown that an N=1 superconformal algebra could be constructed [1], and that the cohomology of the corresponding N=1 BRST charge coincides with the cohomology of the original bosonic string [2,3]. Furthermore, it was shown that the N=1 prescription for calculating scattering amplitudes with this special choice of matter fields produces the usual bosonic string amplitudes [1,3], allowing one to view the bosonic string as a background of N=1 strings.…”

mentioning

confidence: 99%