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# Bulk fields from the boundary OPE

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### Abstract

Previous work has established an equality between the geodesic integral of a free bulk field in AdS and the contribution of the conformal descendants of its dual CFT primary operator to the OPE of two other operators inserted at the endpoints of the geodesic. Working in the context of AdS$$_3$$/CFT$$_2$$, we extend this relation to include all $$1/N$$ corrections to the bulk field obtained by dressing it with i) a $$U(1)$$ current and ii) the CFT stress tensor, and argue it equals the contribution of the Ka\v{c}-Moody/the Virasoro block to the respective boundary OPE. This equality holds for a particular framing of the bulk field to the boundary that involves a split Wilson line.

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###### Journal
2016-10-27
1610.08952