The discussion of renormalization group flows in four-dimensional conformal field theories has recently focused on the a-anomaly. It has recently been shown that there is a monotonic decreasing function which interpolates between the ultraviolet and
infrared fixed points such that Delta a = a_UV - a_IR > 0. The analysis has been extended to weakly relevant and marginal deformations, though there are few explicit examples involving interacting theories. In this paper we examine the a-theorem in the context of the gauged vector model which couples the usual vector model to the Banks-Zaks model. We consider the model to leading order in the 1/N expansion, all orders in the coupling constant lambda, and to second order in g^2. The model has both an IR and UV fixed point, and satisfies Delta a > 0.
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.
