 Gaussian free field level line

A continuum field level line is specified by the harmonic boundary heights it creates and the conditional zero-boundary field remaining on each side. Since a Continuum Gaussian free field is a random distribution, this is not the pointwise set of its zeros. For the height jump appropriate to the Green-function normalization, the zero-height line between opposite Dirichlet heights is chordal ${\mathrm{SLE}}_4$.