Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations

Abstract

We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fields on sphere can be computed exactly in terms of the free field theory on the covering Riemann surface, even for a non-abelian monodromy group. The generalized twist fields are identified with particular primary fields of the W-algebra, and we propose a straightforward way to compute their W-charges. We demonstrate how these exact conformal blocks can be effectively computed using the technique arisen from the gauge theory/CFT correspondence. We discuss also their direct relation with the isomonodromic tau-function for the quasipermutation monodromy data, which can be an encouraging step on the way of definition of generic conformal blocks for W-algebra using the isomonodromy/CFT correspondence.

30 pages, 5 figures

References in corpus (3)

• Correlation functions in conformal Toda field theory I
• Isomonodromic $\tau$-functions and $W_N$ conformal blocks
• Deformations of special geometry: in search of the topological string

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• Second level semi-degenerate fields in W3 Toda theory: matrix element and differential equation
• Twist-field representations of W-algebras, exact conformal blocks and character identities