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arXiv · 1401.6104

Isomonodromic tau-functions from Liouville conformal blocks

N. Iorgov·O. Lisovyy·J. Teschner
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Abstract

The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with $SL(2,\mathbb{C})$-valued monodromy on Riemann surfaces of genus zero with $n$ punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at $c=1$. This implies a similar representation for the isomonodromic tau-function. In the case $n=4$ we thereby get a proof of the relation between tau-functions and conformal blocks discovered in \cite{GIL}. We briefly discuss a possible application of our results to the study of relations between certain $\mathcal{N}=2$ supersymmetric gauge theories and conformal field theory.

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N. Iorgov, O. Lisovyy, J. Teschner. 2014-07-22. Isomonodromic tau-functions from Liouville conformal blocks. https://doi.org/10.1007/s00220-014-2245-0

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