Geodesic
Geometric Properties of $W$-Algebras and the Toda model
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 2, pp. 179-192

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The $W$-algebra minimal models on hyperelliptic Riemann surfaces are constructed. Using a proposal by Polyakov, we reduce the partition function of the Toda field theory on the hyperelliptic surface to a product of partition functions: one of a “free field” theory on the sphere with inserted Toda vertex operators and one of a free scalar field theory with antiperiodic boundary conditions with inserted twist fields.
Keywords: conformal field theory, integrable systems, Toda field theory
Mots-clés : hyperelliptic surfaces. 
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     author = {S. A. Apikyan and M. A. Barsamian and K. J. Efthimiou},
     title = {Geometric {Properties} of $W${-Algebras} and the {Toda} model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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S. A. Apikyan; M. A. Barsamian; K. J. Efthimiou. Geometric Properties of $W$-Algebras and the Toda model. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 2, pp. 179-192. http://geodesic.mathdoc.fr/item/TMF_2004_138_2_a0/