Operator mixing for string states in the D1-D5 CFT near the orbifold point

In the context of the fuzzball program, we investigate deforming the microscopic string description of the D1-D5 system on T-4 x S-1 away from the orbifold point. Using conformal perturbation theory and a generalization of Lunin-Mathur symmetric orbifold technology for computing twist-nontwist correlators developed in a companion paper Burrington et al., arXiv:1211.6689, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting the identified conformal family to isolate other contributions to the four-point function, finding the mixing coefficients, and iterating. For the lowest-lying string modes, this procedure should truncate in a finite number of steps. We check our method by showing how the operator dual to the dilaton does not participate in mixing that would change its conformal dimension, as expected. Next we complete the first stage of the iteration procedure for a low-lying string state of the form partial derivative X partial derivative X partial derivative X partial derivative X and find its mixing coefficient. Our most interesting qualitative result is evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 superconformal field theory must decrease away from the orbifold point while others increase.