W-Algebras Extending \(\widehat{\mathfrak{g}\mathfrak{l}}(1\vert 1)\)

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 36)


We have recently shown that \(\widehat{\mathfrak{g}\mathfrak{l}}\left (1\vert 1\right )\) admits an infinite family of simple current extensions. Here, we review these findings and add explicit free field realizations of the extended algebras. We use them for the computation of leading contributions of the operator product algebra. Amongst others, we find extensions that contain the Feigin–Semikhatov W N (2) algebra at levels k = N(3 − N) ∕ (N − 2) and k = − N + 1 + N − 1 as subalgebras.


Central Charge Operator Product Expansion Conformal Dimension Conformal Field Theory Fusion Rule 
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Copyright information

© Springer Japan 2013

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Department of Theoretical Physics, Research School of Physics and Engineering and Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia

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