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Journal of High Energy Physics

, 2016:181 | Cite as

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

  • P. GavrylenkoEmail author
  • A. Marshakov
Open Access
Regular Article - Theoretical Physics

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.

Keywords

Conformal and W Symmetry Integrable Hierarchies Integrable Equations in Physics 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Department of Mathematics and Laboratory of Mathematical Physics, NRU HSEMoscowRussia
  2. 2.Bogolyubov Institute for Theoretical PhysicsKyivUkraine
  3. 3.Theory Department, Lebedev Physics Institute and Institute for Theoretical and Experimental PhysicsMoscowRussia

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