Geometric Properties of W-Algebras and the Toda model

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Theoretical and Mathematical Physics, ISSN: 0040-5779, Vol: 138, Issue: 2, Page: 151-162

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S. A. Apikyan; M. H. Barsamian; C. J. Efthimiou
Springer Nature
Physics and Astronomy; Mathematics; conformal field theory; integrable systems; Toda field theory; hyperelliptic surfaces; MULTIPOINT CORRELATION-FUNCTIONS; QUANTUM-FIELD THEORY; SYMMETRY; SURFACES; Physics; Multidisciplinary; Physics; Mathematical
article description
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.