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arXiv · 1307.4865

Lax matrix solution of c=1 Conformal Field Theory

Bertrand Eynard·Sylvain Ribault
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Abstract

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 implies that the differential equation is isomonodromic. This provides a justification for the recently observed relation between four-point conformal blocks and solutions of the Painlev\'e VI equation. This also provides a direct way to compute the three-point function of Runkel-Watts theory -- the common $c\rightarrow 1$ limit of Minimal Models and Liouville theory.

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Bertrand Eynard, Sylvain Ribault. 2013-07-18. Lax matrix solution of c=1 Conformal Field Theory. https://doi.org/10.1007/jhep02(2014)059

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