Supersymmetric deformations of F 1 - NS 5 - branes and their exact CFT description

We consider certain classes of operators in the exact conformal field theory SL(2,R) × SU(2) × U(1) describing strings in an AdS3 × S × T 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 N = 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. ∗[email protected] †[email protected] ‡[email protected] ar X iv :0 90 5. 16 23 v2 [ he pth ] 1 7 Se p 20 09