In the context of the fuzzball programme, we investigate deforming the microscopic string description of the D1-D5 system on T^4xS^1 away from the orbifold point. Using conformal perturbation theory and a generalization of Lunin-Mathur symmetric orbi
fold technology for computing twist-nontwist correlators developed in a companion work, 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 X partial X barpartial X barpartial X and find its mixing coefficient. Our main 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 SCFT must decrease away from the orbifold point while others increase.
We consider general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group, and generalize the Lunin-Mathur covering space technique in two ways. First, we consider excitations of twist operators by modes of
fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. We work two examples, one using a simple bosonic CFT, and one using the D1-D5 CFT at the orbifold point. We show that the resulting correlators have the correct form for a 2D CFT.
Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent zgeq 1. We numerically explore a dilaton-Einstein-Maxwell model admit
ting such backgrounds as solutions. Such backgrounds are characterized by a temperature T and chemical potential mu, and we find how to embed these solutions into AdS for a range of values of z and d. We find no thermal instability going from the (Tllmu) to the (Tggmu) regimes, regardless of the dimension, and find that the solutions smoothly interpolate between the Lifshitz-like behaviour and the relativistic AdS-like behaviour. We exploit some conserved quantities to find a relationship between the energy density E, entropy density s, and number density n, E=frac{d}{d+1}(Ts+nmu), as is required by the isometries of AdS_{d+2}. Finally, in the (Tllmu) regime the entropy density is found to satisfy a power law s propto c T^{d/z} mu^{(z-1)d/z}, and we numerically explore the dependence of the constant c, a measure of the number of degrees of freedom, on d and z.
