Bertrand Eynard, Sylvain Ribault
To a correlation function in a two-dimensional conformal field theory with the central charge c=1, we associate a matrix differential equation \Psi'=L\Psi, where the Lax matrix L is a matrix square root of the energy-momentum tensor. Then local conformal symmetry translates into isomonodromy of the differential equation. This provides a justification for the recently observed relation between four-point conformal blocks and solutions of the Painleve VI equation. This also provides a direct way to compute the three-point function of Runkel-Watts theory - the common c->1 limit of Minimal Models and Liouville theory.
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http://arxiv.org/abs/1307.4865
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