Contour lines of the two-dimensional discrete Gaussian free field

We prove that the chordal contour lines of the discrete Gaussian free field converge to forms of SLE(4). Specifically, there is a constant lambda > 0 such that when h is an interpolation of the discrete Gaussian free field on a Jordan domain-with boundary values -lambda on one boundary arc and lambda on the complementary arc-the zero level line of h joining the endpoints of these arcs converges to SLE(4) as the domain grows larger. If instead the boundary values are -a < 0 on the first arc and b > 0 on the complementary arc, then the convergence is to SLE(4; a/lambda - 1, b/lambda - 1), a variant of SLE(4).