# Lax matrix solution of c=1 Conformal Field Theory

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 Painlevé 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.
Document type :
Journal articles
Domain :

https://hal-cea.archives-ouvertes.fr/cea-01062772
Contributor : Emmanuelle de Laborderie <>
Submitted on : Wednesday, September 10, 2014 - 3:08:31 PM
Last modification on : Friday, May 10, 2019 - 4:38:15 PM

### Citation

Bertrand Eynard, Sylvain Ribault. Lax matrix solution of c=1 Conformal Field Theory. Journal of High Energy Physics, Springer, 2014, 2014, pp.059. ⟨10.1007/JHEP02(2014)059⟩. ⟨cea-01062772⟩

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