The geometry of Casimir W-algebras
Keyword(s):
Let \mathfrak{g}𝔤 be a simply laced Lie algebra, \widehat{\mathfrak{g}}_1𝔤̂1 the corresponding affine Lie algebra at level one, and \mathcal{W}(\mathfrak{g})𝒲(𝔤) the corresponding Casimir W-algebra. We consider \mathcal{W}(\mathfrak{g})𝒲(𝔤)-symmetric conformal field theory on the Riemann sphere. To a number of \mathcal{W}(\mathfrak{g})𝒲(𝔤)-primary fields, we associate a Fuchsian differential system. We compute correlation functions of \widehat{\mathfrak{g}}_1𝔤̂1-currents in terms of solutions of that system, and construct the bundle where these objects live. We argue that cycles on that bundle correspond to parameters of the conformal blocks of the W-algebra, equivalently to moduli of the Fuchsian system.
1993 ◽
Vol 08
(23)
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pp. 4031-4053
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2002 ◽
Vol 35
(12)
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pp. 2985-3007
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1993 ◽
Vol 08
(31)
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pp. 5537-5561
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2007 ◽
Vol 2007
(10)
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pp. P10004-P10004
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1994 ◽
Vol 09
(14)
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pp. 2451-2466
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Keyword(s):
2006 ◽
Vol 40
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pp. 156-162
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Keyword(s):
1997 ◽
Vol 12
(21)
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pp. 3723-3738
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