Localization of Affine W-Algebras

Communications in Mathematical Physics volume 335, pages143–182(2015)Cite this article

Abstract

We introduce the notion of an asymptotic algebra of chiral differential operators. We then construct, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra, thereby proving a localization theorem for affine W-algebras at the critical level.

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Author information

Affiliations

  1. RIMS, Kyoto University, Kyoto, 606-8502, Japan

    T. Arakawa

  2. Department of Mathematics and International Laboratory of Representation Theory and Mathematical Physics, National Research University Higher School of Economics, 20 Myasnitskaya Ulitsa, Moscow, 101000, Russia

    T. Kuwabara

  3. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    F. Malikov

Authors
  1. T. Arakawa
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  2. T. Kuwabara
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  3. F. Malikov
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Corresponding author

Correspondence to T. Kuwabara.

Additional information

T. Arakawa is partially supported by the JSPS Grant-in-Aid for Scientific Research (B) No. 20340007 and the JSPS Grant-in-Aid for challenging Exploratory Research No. 23654006.

T. Kuwabara was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST)(2011-0027952).

F. Malikov is partially supported by an NSF grant.

Communicated by Y. Kawahigashi

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Arakawa, T., Kuwabara, T. & Malikov, F. Localization of Affine W-Algebras. Commun. Math. Phys. 335, 143–182 (2015). https://doi.org/10.1007/s00220-014-2183-x

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Keywords

  • Spectral Sequence
  • Complete Intersection
  • Vertex Algebra
  • Poisson Algebra
  • Hamiltonian Reduction