Construction of the K = 8 fractional superconformal algebras

Argyres, Philip C.; Grochocinski, J.M.; Tye, S.‐H. Henry

doi:10.1016/0550-3213(93)90154-h

Cited by 6 publications

(17 citation statements)

References 23 publications

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“…One interpretation is this implies a compactification of two transverse dimensions. 10 Let us choose the 9 Similar conclusions have been reached by K. Dienes and P. Argyres for different reasons. They have, in fact, found thetafunction expressions for the B boson K -and B fermion K -subsectors.…”

Section: B)mentioning

confidence: 95%

Aspects of fractional superstrings

Cleaver

Rosenthal

1995

Commun.Math. Phys.

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We investigate some issues relating to recently proposed fractional superstring theories with D critical < 10. Using the factorization approach of Gepner and Qiu, we systematically rederive the partition functions of the K = 4, 8, and 16 theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the K = 4 model are found. Uniqueness of the twist field, φ K/4 K/4 , as source of spacetime fermions is demonstrated. Last, we derive a linear (rather than quadratic) relationship between the required conformal anomaly and the conformal dimension of the supercurrent ghost.

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Section: B)mentioning

confidence: 95%

Aspects of fractional superstrings

Cleaver

Rosenthal

1995

Commun.Math. Phys.

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“…The first is that the complexity of these theories increases considerably with increasing K. Although the world-sheet fractional supersymmetry algebra is non-local, the Z 4 parafermion fields that appear in the K = 4 FSS can be simply represented by free bosons, which enables the calculations to be simplified tremendously. This is not the case in the K = 8 and K = 16 theories [10,11]. Furthermore, a close examination shows that the appropriate world-sheet fractional supersymmetry algebra for the K = 8 theory contains two spin-13/5 currents in addition to the spin-6/5 current [11], which further complicate the analysis.…”

mentioning

confidence: 97%

Low-lying states of the six-dimensional fractional superstring

Argyres

Lyman²,

Tye³

1992

Phys. Rev. D

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The K = 4 fractional superstring Fock space is constructed in terms of Z 4 parafermions and free bosons. The bosonization of the Z 4 parafermion theory and the generalized commutation relations satisfied by the modes of various parafermion fields are reviewed. In this preliminary analysis, we describe a Fock space which is simply a tensor product of Z 4 parafermion and free boson Fock spaces. It is larger than the Lorentz-covariant Fock space indicated by the fractional superstring partition function. We derive the form of the fractional superconformal algebra that may be used as the constraint algebra for the physical states of the FSS. Issues concerning the associativity, modings and braiding properties of the fractional superconformal algebra are also discussed. The use of the constraint algebra to obtain physical state conditions on the spectrum is illustrated by an application to the massless fermions and bosons of the K = 4 fractional superstring. However, we fail to generalize these considerations to the massive states. This means that the appropriate constraint algebra on the fractional superstring Fock space remains to be found. Some possible ways of doing this are discussed. * 1The case K = 2 (D = 10) corresponds to the superstring. The new theories are those with K > 2; for K = 4, 8 and 16 we have the integer critical dimensions D = 6, 4 and 3, respectively.In this paper we will concentrate exclusively on the simplest case after the (K = 2) superstring, the K = 4 FSS. The reasons for this are twofold. The first is that the complexity of these theories increases considerably with increasing K. Although the world-sheet fractional supersymmetry algebra is non-local, the Z 4 parafermion fields that appear in the K = 4 FSS can be simply represented by free bosons, which enables the calculations to be simplified tremendously. This is not the case in the K = 8 and K = 16 theories [10,11]. Furthermore, a close examination shows that the appropriate world-sheet fractional supersymmetry algebra for the K = 8 theory contains two spin-13/5 currents in addition to the spin-6/5 current [11], which further complicate the analysis. The second reason for our emphasis on the K = 4 FSS is because it is potentially the most interesting one from the phenomenological point of view. As argued in [12,13], the requirements of quantum mechanics, Lorentz invariance and locality suggest that the K = 4 FSS may be automatically compactified from six to four space-time dimensions. Furthermore, as argued in [12], the compactification from the critical dimension 6 to the natural dimension 4 offers the possibility of the construction of heterotic type K = 4 FSS models that have chiral space-time fermions. This is encouraging, since the K = 4 FSS, because of its relative simplicity, affords the best prospect for detailed examination in the near future.Let us highlight some of the similarities and differences between the K = 4 FSS and the superstring. In the superstring, the world-sheet superpartner of the space-time coordinate boson X µ...

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“…The representation theory of the other simple series of algebras based on the su(2) K models, though non-abelianly braided in general, have been more intensively studied [12]. Since su(2) K = so(3) K/2 all these models (trivially) have representations with so(2, 1) Lorentz symmetry.…”

Section: Discussion and Outlookmentioning

confidence: 99%

“…This world-sheet algebra is associated with the su(2) 4 Wess-ZuminoWitten (WZW) model as explained in Appendix B. In general, one can construct fractional algebras associated in the same way to WZW models based on any Lie algebra [6,1,12]. For example, the algebra based on su(2) 1 is simply the Virasoro algebra, and its associated string is the bosonic string; associated with su(2) 2 is the super-Virasoro algebra which underlies the ordinary superstring.…”

Section: Discussion and Outlookmentioning

confidence: 99%

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Tree scattering amplitudes of the spin-43fractional superstring. I. The untwisted sectors

Argyres

Tye

1994

Phys. Rev. D

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Scattering amplitudes of the spin-4/3 fractional superstring are shown to satisfy spurious state decoupling and cyclic symmetry (duality) at tree-level in the string perturbation expansion. This fractional superstring is characterized by the spin-4/3 fractional superconformal algebra-a parafermionic algebra studied by Zamolodchikov and Fateev involving chiral spin-4/3 currents on the world-sheet in addition to the stress-energy tensor. Examples of tree scattering amplitudes are calculated in an explicit c = 5 representation of this fractional superconformal algebra realized in terms of free bosons on the string worldsheet. The target space of this model is three-dimensional flat Minkowski spacetime with a level-2 Kač-Moody so(2, 1) internal symmetry, and has bosons and fermions in its spectrum. Its closed string version contains a graviton in its spectrum. Tree-level unitarity (i.e., the no-ghost theorem for spacetime bosonic physical states) can be shown for this model. Since the critical central charge of the spin-4/3 fractional superstring theory is 10, this c = 5 representation cannot be consistent at the string loop level. The existence of a critical fractional superstring containing a four-dimensional space-time remains an open question. *

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Construction of the K = 8 fractional superconformal algebras

Cited by 6 publications

References 23 publications

Aspects of fractional superstrings

Aspects of fractional superstrings

Low-lying states of the six-dimensional fractional superstring

Tree scattering amplitudes of the spin-43fractional superstring. I. The untwisted sectors

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