TY - EJOUR AU - Iorgov, N. AU - Lisovyy, O. AU - Teschner, J. TI - Isomonodromic tau-functions from Liouville conformal blocks IS - DESY-14-012 M1 - DESY-2014-02606 M1 - DESY-14-012 M1 - arXiv:1401.6104 PY - 2014 N1 - 29 pages, 4 figures AB - The goal of this note is to show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,\mathbbC)-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 . We briefly discuss a possible application of our results to the study of relations between certain <i>N</i>=2 supersymmetric gauge theories and conformal field theory. KW - gauge field theory: supersymmetry (INSPIRE) KW - field theory: Liouville (INSPIRE) KW - field theory: conformal (INSPIRE) KW - conformal block (INSPIRE) KW - tau-function (INSPIRE) KW - Riemann surface (INSPIRE) KW - monodromy (INSPIRE) LB - PUB:(DE-HGF)25 ; PUB:(DE-HGF)15 UR - https://bib-pubdb1.desy.de/record/168709 ER -