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TMF, 2015, Volume 182, Number 3, Pages 355–372 (Mi tmf8644)  

This article is cited in 1 scientific paper (total in 1 paper)

$W$-algebras and higher analogues of the Knizhnik–Zamolodchikov equations

D. V. Artamonova*, V. A. Golubevab

a Lomonosov Moscow State University, Moscow, Russia
b Moscow Aviation Institute (National Research University), Moscow, Russia

Abstract: The key role in the derivation of the Knizhnik–Zamolodchikov equations in the Wess–Zumino–Witten model is played by the energy–momentum tensor, which is constructed from a second-order Casimir element in the universal enveloping algebra of the corresponding Lie algebra. We investigate the possibility of constructing analogues of Knizhnik–Zamolodchikov equations using higher-order central elements. We consider the Casimir element of the third order for the Lie algebra $\mathfrak{sl}_N$ and of the fourth order for $\mathfrak{o}_N$. The construction is impossible in the first case, but we succeed in obtaining the sought equation in the second case.

Keywords: Casimir element, $W$-algebra, Kniznik–Zamolodchikov equation, commutative Pfaffian

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation МК-4594.2013.1

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/tmf8644

Full text: PDF file (559 kB)
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English version:
Theoretical and Mathematical Physics, 2015, 182:3, 313–328

Bibliographic databases:

PACS: 02.20.Tw
MSC: 81R10
Received: 20.01.2014
Revised: 28.09.2014

Citation: D. V. Artamonov, V. A. Golubeva, “$W$-algebras and higher analogues of the Knizhnik–Zamolodchikov equations”, TMF, 182:3 (2015), 355–372; Theoret. and Math. Phys., 182:3 (2015), 313–328

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Artamonov D.V., “Introduction To Finite W-Algebras”, Bol. Mat., 23:2 (2016), 165–219  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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