Transformed SLE driving function ($d{\tilde{\xi }}_t=\sqrt{\kappa }{\varphi }_t^{\prime }({\xi }_t)d{W}_t+(\kappa /2-3){\varphi }_t^{\prime \prime }({\xi }_t)dt$)

Apply the Itô formula to the transformed Loewner driving function ${\tilde{\xi }}_t={\varphi }_t(\sqrt{\kappa }{W}_t)$. The conformal conjugacy derivative for the chordal Loewner equation cancels the Itô drift exactly when $\kappa =6$. Its quadratic variation is $\kappa {\int }_0^t{\varphi }_s^{\prime }({\xi }_s{)}^{2}ds$.