Supersymmetric deformations of F1-NS5-branes and their exact CFT description

We consider certain classes of operators in the exact conformal field theory SL(2,) × SU(2) × U(1) ⁴ describing strings in an AdS ₃ × S ³ × ⁴ geometry supported by Neveu-Schwarz 3-form fluxes. This background arises in the near-horizon limit of a system of NS5-branes wrapped on a 4-torus and F1-branes smeared on the 4-torus when both types of branes are located at the same point in their common transverse space. We find a class of operators that lead to spacetime supersymmetric deformations. It is remarkable that most of these operators are not chiral primary with respect to the = 2 superconformal algebra on the worldsheet. A subset of these worldsheet conformal field theory deformations admits an interpretation either as a geometric deformation of the brane system or as a deformation of the distribution of the F1-branes, viewed as smooth instantons, inside the wrapped NS5-brane worldvolume. The 2-dimensional conformal field theory, however, seems to lack operators corresponding to arbitrary NS5-brane deformations, in contrast to pure NS5-brane systems where all geometric deformations can be accounted for by chiral primary operators.