  We calculate all multipoint correlation functions of all local bond
modifications in the two-dimensional Abelian sandpile model, both at the
critical point, and in the model with dissipation. The set of local bond
modifications includes, as the most physically interesting case, all weakly
allowed cluster variables. The correlation functions show that all local bond
modifications have scaling dimension two, and can be written as linear
combinations of operators in the central charge -2 logarithmic conformal field
theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in
Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the
coefficients of the operators, and describe methods that allow their rapid
calculation. We determine the fields associated with adding or removing bonds,
both in the bulk, and along open and closed boundaries; some bond defects have
scaling dimension two, while others have scaling dimension four. We also
determine the corrections to bulk probabilities for local bond modifications
near open and closed boundaries.
