On generalized fractional superstring theory

Chakir, H.; El-Fallah, A.; Saidi, E. H.

doi:10.1088/0264-9381/14/8/007

Cited by 3 publications

(5 citation statements)

References 16 publications

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“…To illustrate how things work in practice let us consider an example. The method we will present herebelow applies to all Z k parafermionic models as well as others such as the Tye et al symmetries [20,21 ].…”

Section: D Fssmentioning

confidence: 99%

Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of ${\mathrm{AdS}}_3$

Benkaddour¹,

Rhalami²,

Saidi³

2001

Eur. Phys. J. C

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Using recent results on strings on AdS 3 × N d , where N is a d-dimensional compact manifold, we re-examine the derivation of the non trivial extension of the (1+2)dimensional-Poincaré algebra obtained by Rausch de Traubenberg and Slupinsky, refs[1]and [29] . We show by explicit computation that this new extension is a special kind of fractional supersymmetric algebra which may be derived from the deformation of the conformal structure living on the boundary of AdS 3 . The two so(1, 2) Lorentz modules of spin ± 1 k used in building of the generalisation of the (1+2) Poincaré algebra are re-interpreted in our analysis as highest weight representations of the left and right Virasoro symmetries on the boundary of AdS 3 . We also complete known results on 2d-fractional supersymmetry by using spectral flow of affine Kac-Moody and superconformal symmetries. Finally we make preliminary comments on the trick of introducing Fth-roots of g-modules to generalise the so(1, 2) result to higher rank Lie algebras g.

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Section: D Fssmentioning

confidence: 99%

Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of ${\mathrm{AdS}}_3$

Benkaddour¹,

Rhalami²,

Saidi³

2001

Eur. Phys. J. C

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“…For N > 2, however, there are in total (N −1) ways of performing the decompactification. For the case N = 3, for example, we have two possibilities, one of them is used in [11], namely…”

Section: More On the Parafermions φ λ µmentioning

confidence: 99%

“…one can calculate the critical dimension d(N, K, n) of this G K fractional superstring model by following the same method as used in section 2. Straightforward calculations lead to 1)) model of [11]. It should be noted here that the derivation of equation ( 43) is based upon demanding the vector states of the spectrum of the generalized fractional superstring models to be massless.…”

Section: More On the Parafermions φ λ µmentioning

confidence: 99%

“…These kinds of models are expected to exhibit a rich symmetry on the string worldsheet generated by N −1 fractional supercurrents G j of conformal weights h(G j ) = j + N/(N + K) and N − 1 bosonic W -currents W j +1 of conformal weight h(W j +1 ) = j + 1. We shall refer to this symmetry as fractional super-Wsymmetry [10,11]. Note that the existence of N − 1 fractional supercurrents G j is related to the existence of N − 1 energy operators ε j of conformal weight h(ε j ) = N/(K + N) in the adjoint representation of the SU K (N )/U (1) N−1 symmetry.…”

Section: Introductionmentioning

confidence: 99%

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On generalized fractional superstring models and the associative division algebras

Fallah¹,

Saidi²,

Dick³

1999

Class. Quantum Grav.

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A special subset of generalized fractional superstring models extending those of Argyres et al is studied. This subset concerns models based on SUK (K )/U (1)K -1 Gepner parafermions. It is shown that there exists a remarkable link between generalized fractional superstrings based on SUK (K )/U (1)K -1 Wess-Zumino-Witten theory with K = 2, 3 and 5, and the associative division algebras. These models have critical dimensions 10, 2 × 5 and 4 × 3, respectively, and are in one-to-one correspondence with real, Kähler, and hyper-Kähler target spaces. Moreover, we obtain field-theoretical realizations of c 0 = 4 super-W 3 and c 0 = 12 super-W 5 symmetries based on the K = 3 and 5 parafermions. It is also shown that the conformal anomaly of the parafermion ghosts of the worldsheet fractional supersymmetry is Cparaghost = 15 - K 2 .

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“…The existence of a consistent fractional superstring theory is quite significant because we totally lost the reason why we can ignore the possibility of this string theory. Since there are infinitely many kinds of the fractional superstrings (which are essentially related to the classification of Kac-Moody algebra) [58], this implication opens a broad possibility of string theory.…”

Section: Introductionmentioning

confidence: 99%

Fractional supersymmetric Liouville theory and the multi-cut matrix models

Irie

2009

Nuclear Physics B

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We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p, q) minimal fractional superstring theories appear in the Z k -symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators. * Every odd k-cut model (i.e. k is odd) has the same contour integral as even 2k-cut models have. They are, however, physically different systems because their Liouville directions e −bφ = Re (ζ bos ) = Re (ζ k ) are different. 5 Only when k ≤ 2, the two-matrix models can include the one-matrix models as the special case of the system because the Gaussian potential V (y) = y 2 which is necessary for the reduction into one-matrix model is forbidden in the higher Z k symmetric case. 6 We cannot use this measure when the number of the matrices in the model is odd, which includes one-matrix models and matrix quantum mechanics. 7 This kind of matrix contour integral is also observed in the supermatrix description of the type 0 superstrings [57].

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On generalized fractional superstring theory

Cited by 3 publications

References 16 publications

Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of ${\mathrm{AdS}}_3$

Non-trivial extension of the (1+2)-Poincaré algebra and conformal invariance on the boundary of ${\mathrm{AdS}}_3$

On generalized fractional superstring models and the associative division algebras

Fractional supersymmetric Liouville theory and the multi-cut matrix models

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