Conformal field theory correlations in the Abelian sandpile model

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 2, 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 2, while others have scaling dimension 4. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.