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W-algebras as coset vertex algebras

  • Tomoyuki Arakawa
  • Thomas CreutzigEmail author
  • Andrew R. Linshaw
Article
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Abstract

We prove the long-standing conjecture on the coset construction of the minimal series principal W-algebras of ADE types in full generality. We do this by first establishing Feigin’s conjecture on the coset realization of the universal principal W-algebras, which are not necessarily simple. As consequences, the unitarity of the “discrete series” of principal W-algebras is established, a second coset realization of rational and unitary W-algebras of type A and D are given and the rationality of Kazama–Suzuki coset vertex superalgebras is derived.

Notes

Acknowledgements

This work started when we visited Perimeter Institute for Theoretical Physics, Canada, for the conference “Exact operator algebras in superconformal field theories” in December 2016. We thank the organizers of the conference and the institute. The first named author would like to thank MIT for its hospitality during his visit from February 2016 to January 2018.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Tomoyuki Arakawa
    • 1
  • Thomas Creutzig
    • 2
    Email author
  • Andrew R. Linshaw
    • 3
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada
  3. 3.Department of MathematicsUniversity of DenverDenverUSA

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