Wilson line networks in AdS2 are reconstructed from boundary conformal blocks, and 3-point scalar Witten diagrams decompose into sums of such networks.
Gravitational Wilson lines in AdS$_{\bf 3}$
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abstract
The construction of gravitational Wilson lines in the Chern-Simons formulation of $AdS_3$ gravity in terms of composite operators in the dual boundary conformal field theory is reviewed. New evidence is presented that the Wilson line, dimensionally regularized and suitably renormalized, behaves as a bi-local operator of two conformal primaries whose dimension is predicted by SL(2,R) current algebra.
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Holographic reconstruction for AdS Wilson line networks and scalar Witten diagrams
Wilson line networks in AdS2 are reconstructed from boundary conformal blocks, and 3-point scalar Witten diagrams decompose into sums of such networks.