Chordal SLE4 (${\mathrm{SLE}}_4$)

Chordal SLE at parameter four has driver $2{\beta }_t$ in half-plane-capacity time. The Itô formula makes the imaginary part of $\log (g_t(z)-W_t)$ drift-free, a feature used in the SLE4 coupling with a Gaussian free field. The trace is simple and avoids fixed nonzero boundary points.