  We report on the exact computation of the scaling form of the 1-point
function, on the upper-half plane, of the height 2 variable in the
two-dimensional Abelian sandpile model. By comparing the open versus the closed
boundary condition, we find that the scaling field associated to the height 2
is a logarithmic scalar field of scaling dimension 2, belonging to a c=-2
logarithmic conformal field theory. This identification is confirmed by
numerical simulations and extended to the height 3 and 4 variables, which
exhibit the same scaling form. Using the conformal setting, we make precise
proposals for the bulk 2-point functions of all height variables.
