Gravity on $AdS_3$ and flat connections in the boundary CFT

Details Gravity on $AdS_3$ and flat connections in the boundary CFT Gravity on $AdS_3$ and flat connections in the boundary CFT

2001-01-17

arxiv.org/abs/hep-th/0101118v2

Physics

High Energy Physics

High Energy Physics - Theory

35 pages, harvmac, references added

Scientific paper

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 D1-D5 state with angular momentum, observing relations between scales in the microscopic theory and scales in the geometry.

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