Gravity on AdS3 and flat connections in the boundary CFT

We consider the CFT that arises from the D1-D5 system in the presence of a constant background gauge potential which couples to the R-charge of the theory: this potential effectively changes the periodicities of the fermions. By the AdS/CFT correspondence, the effect of this connnection should be obtained by finding a smooth solution to the vector field in AdS space which couples to the constant mode of the R-current in the CFT. We investigate such solutions for small values of the connection, and contrast these with spacetimes which have ‘Wilson lines for the bulk ’ – spacetimes that are locally AdS times a sphere but have a global deformation. The latter class are in general singular spacetimes. We comment on some aspects of the recently found geometries corresponding to the D1D5 state with angular momentum, observing relations between scales in the microscopic theory and scales in the geometry.