W-Algebras
W-Algebras
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DOI：
10.1515/zna-1997-1-221
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
L. Raifeartaigh
中科院分区：
文献类型：
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作者：
L. Raifeartaigh
摘要W-代数是Virasoro代数的初等域的多项式扩张，它们以自然的方式出现在二维可积系统中，特别是KdV和户田系统。它们在这些理论中的出现可以追溯到当某些第一类约束放在Kac-Moody代数上时它们是剩余对称代数。特别是，他们的发生在2维户田理论解释的事实，即户田理论可以被视为约束Wess-Zumino-Novikov-Witten（WZNW）理论。这种第一类约束的WZNW理论的一般形式进行了研究，并示出导致更广泛的一类二维可积系统，所有这些都有W-代数作为对称代数。
Abstract W-algebras are defined as polynomial extensions of the Virasoro algebra by primary fields, and they occur in a natural manner in the context of two-dimensional integrable systems, notably in the KdV and Toda systems. Their occurrence in those theories can be traced to their being the residual symmetry algebras when certain first-class constraints are placed on Kac-Moody algebras. In particular, their occurrence in 2-dimensional Toda theories is explained by the fact that the Toda theories can be regarded as constrained Wess-Zumino-Novikov-Witten (WZNW) theories. The general form of such first-class constraint for WZNW theories is investigated, and is shown to lead to a wider class of two-dimensional integrable systems, all of which have W-algebras as symmetry algebras.