## Abstract

Abstract: We study the solution of the Schlesinger system for the 4-point slN isomonodromy problem and conjecture an expression for the isomonodromic τ-function in terms of 2d conformal field theory beyond the known N = 2 Painlevé VI case. We show that this relation can be used as an alternative definition of conformal blocks for the W_{N} algebra and argue that the infinite number of arbitrary constants arising in the algebraic construction of W_{N} conformal block can be expressed in terms of only a finite set of parameters of the monodromy data of rank N Fuchsian system with three regular singular points. We check this definition explicitly for the known conformal blocks of the W_{3} algebra and demonstrate its consistency with the conjectured form of the structure constants.

Original language | English |
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Article number | 167 |

Journal | Journal of High Energy Physics |

Volume | 2015 |

Issue number | 9 |

DOIs | |

Publication status | Published - 30 Sep 2015 |

Externally published | Yes |

## Keywords

- Conformal and W Symmetry
- Integrable Equations in Physics
- Integrable Hierarchies

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