Singular Dimensions¶of the N= 2 Superconformal Algebras II:¶The Twisted N= 2 Algebra

Dörrzapf, Matthias; Gato-Rivera, Beatriz

doi:10.1007/pl00005566

Cited by 17 publications

(26 citation statements)

References 27 publications

(55 reference statements)

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“…In other words, a singular vector is already completely determined once we have found just the few coefficients with respect to the ordering kernel. In this way we can easily obtain product expressions for descendant singular vectors [13] and also solve the question for which cases descendant singular vectors vanish. The framework can easily be understood using the example of the Virasoro algebra where the ordering kernel always has size one and therefore Virasoro singular vectors at the same level in the sameVerma module are always proportional.…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

“…This case needs a separate consideration. The application of the adapted ordering method to the twisted N = 2 algebra will be the subject of a forthcoming paper [13].…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

“…The results obtained will be translated finally to the Neveu-Schwarz and to the Ramond N = 2 algebras. In a future publication we will further apply these ideas to the twisted N = 2 superconformal algebra [13].…”

Section: Introductionmentioning

confidence: 99%

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Singular Dimensions of the¶N= 2 Superconformal Algebras. I

Dörrzapf

Gato-Rivera

1999

Comm Math Phys

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Verma modules of superconfomal algebras can have singular vector spaces with dimensions greater than 1. Following a method developed for the Virasoro algebra by Kent, we introduce the concept of adapted orderings on superconformal algebras. We prove several general results on the ordering kernels associated to the adapted orderings and show that the size of an ordering kernel implies an upper limit for the dimension of a singular vector space. We apply this method to the topological N = 2 algebra and obtain the maximal dimensions of the singular vector spaces in the topological Verma modules: 0, 1, 2 or 3 depending on the type of Verma module and the type of singular vector. As a consequence we prove the conjecture of Gato-Rivera and Rosado on the possible existing types of topological singular vectors (4 in chiral Verma modules and 29 in complete Verma modules). Interestingly, we have found two-dimensional spaces of singular vectors at level 1. Finally, by using the topological twists and the spectral flows, we also obtain the maximal dimensions of the singular vector spaces for the Neveu-Schwarz N = 2 algebra (0, 1 or 2) and for the Ramond N = 2 algebra (0, 1, 2 or 3).

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Section: Conclusion and Prospectsmentioning

confidence: 99%

“…This case needs a separate consideration. The application of the adapted ordering method to the twisted N = 2 algebra will be the subject of a forthcoming paper [13].…”

Section: Conclusion and Prospectsmentioning

confidence: 99%

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Singular Dimensions of the¶N= 2 Superconformal Algebras. I

Dörrzapf

Gato-Rivera

1999

Comm Math Phys

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“…Since then, there appeared many papers on these algebras, and also, many interesting results were obtained (e.g., Refs. [2,3,6] and the references therein). In the present paper, we shall consider the twisted N = 2 sector.…”

Section: Introductionmentioning

confidence: 97%