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A newN= 6 superconformal algebra

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Abstract

In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO 6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The commutation relations of this algebra, which we will refer to asCK 6, are represented by short distance operator product expansions (OPE). We constructCK 6, as a subalgebra of theSO(6) superconformal algebra K6, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK 6 has no nontrivial central extensions.

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Authors and Affiliations

  1. Department of Mathematics, National Cheng-Kung University, Tainan, Taiwan

    Shun-Jen Cheng

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Victor G. Kac

Authors
  1. Shun-Jen Cheng
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  2. Victor G. Kac
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Corresponding authors

Correspondence to Shun-Jen Cheng or Victor G. Kac.

Additional information

Partially supported by NSC grant 85-2121-M-006-019 of the ROC.

Partially supported by NSF grant DMS-9622870.

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Cheng, SJ., Kac, V.G. A newN= 6 superconformal algebra. Commun. Math. Phys. 186, 219–231 (1997). https://doi.org/10.1007/BF02885679

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  • DOI: https://doi.org/10.1007/BF02885679

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