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We consider the D1D5 CFT near the orbifold point and develop methods for computing the mixing of untwisted operators to first order by using the OPE on the covering surface. We argue that the OPE on the cover encodes both the structure constants for the orbifold CFT and the explicit form of the mixing operators. We show this explicitly for some example operators. We start by considering a family of operators dual to supergravity modes, and show that the OPE implies that there is no shift in the anomalous dimension to first order, as expected. We specialize to the operator dual to the dilaton, and show that the leading order singularity in the OPE reproduces the correct structure constant. Finally, we consider an unprotected operator of conformal dimension (2,2), and show that the leading order singularity and one of the subleading singularities both reproduce the correct structure constant. We check that the operator produced at subleading order using the OPE method is correct by calculating a number of three point functions using a Mathematica package we developed. Further development of this OPE technique should lead to more efficient calculations for the D1D5 CFT perturbed away from the orbifold point.
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