Bulk fields from the boundary OPE

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 the AdS${}_3$/CFT${}_2$ correspondence, we extend this relation to include the $1/N$ corrections to the bulk field obtained by dressing it with i) a $U(1)$ current and ii) the CFT stress tensor. In the former case, we argue that the contribution of the Kač-Moody descendants to the respective boundary OPE equals the geodesic integral of a particular $U(1)$-dressed bulk field, which is framed to the boundary via a split Wilson line. In the latter case, we compute the gravitational $1/N$ corrections to the bulk field in various gauges, and then write a CFT expression for a putative bulk field whose geodesic integral captures the contribution of Virasoro descendants to the OPE of interest. We comment on the bulk interpretation of this expression.

Added a detailed derivation of the bulk field in radial gauge, an appendix, references and various comments and cosmetic changes

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• Kinematic space for conical defects
• The Probe of Curvature in the Lorentzian AdS${}_2$/CFT${}_1$ Correspondence
• Entanglement entropy and kinematic space in BCFT and RG flow
• Quantum Information Approaches to Quantum Gravity