Dressing bulk fields in AdS${}_3$

Abstract

We study a set of CFT operators suitable for reconstructing a charged bulk scalar field $\varphi$ in AdS${}_3$ (dual to an operator $\mathcal{O}$ of dimension $\Delta$ in the CFT) in the presence of a conserved spin-$n$ current in the CFT. One has to sum a tower of smeared non-primary scalars ${\partial }_{+}^m{J}^{(m)}$, where $J^{(m)}$ are primaries with twist $\Delta$ and spin $m$ built from $\mathcal{O}$ and the current. The coefficients of these operators can be fixed by demanding that bulk correlators are well-defined: with a simple ansatz this requirement allows us to calculate bulk correlators directly from the CFT. They are built from specific polynomials of the kinematic invariants up to a freedom to make field redefinitions. To order $1/N$ this procedure captures the dressing of the bulk scalar field by a radial generalized Wilson line.

LaTeX, one figure, 28 pages

References in corpus (5)

• Holographic representation of local bulk operators
• Constructing local bulk observables in interacting AdS/CFT
• Observables, gravitational dressing, and obstructions to locality and subsystems
• CFT representation of interacting bulk gauge fields in AdS
• Holographic Representation of Higher Spin Gauge Fields

Cited by in corpus (2)

• Reconstructing bulk equation of motion using CFT modular Hamiltonians
• Dressing bulk spinor fields in AdS${}_3$