Connection Problem of Knizhnik-Zamolodchikov Equation on Moduli Space ${\mathcal M}_{0,5}$

Abstract: In this article, we consider the connection problem of the KZ (Knizhnik-Zamolodchikov) equation on the moduli space $\cM_{0,5}$, and show that the connection matrices are expressed in terms of the Drinfel'd associator. As the compatibility condition on the connection problem, we have the pentagon relation for the Drinfeld associators. As an application of the connection problem, we derive the five term relation for dilogarithms.