Boundary-to-bulk maps for AdS causal wedges and RG flow

Abstract

We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS${}_{d+1}$ down to the unitary bound $\Delta =(d-2)/2$. That is to say, we construct the `smearing functions' $K$ of HKLL but with different boundary conditions where both dimensions ${\Delta }_{+}$ and ${\Delta }_{-}$ are taken into account. More precisely, we impose Robin boundary conditions, which interpolate between Dirichlet and Neumann boundary conditions and we give explicit expressions for the distributional kernel $K$ with spacelike support. This flow between boundary conditions is known to be captured in the boundary by adding a double-trace deformation to the CFT. Indeed, we explicitly show that using $K$ there is a consistent and explicit map from a Wightman function of the boundary QFT to a Wightman function of the bulk theory. In order to accomplish this we have to study first the microlocal properties of the boundary two-point function of the perturbed CFT and prove its wavefront set satisfies the microlocal spectrum condition. This permits to assert that $K$ and the boundary two-point function can be multiplied as distributions.

arXiv comment26 pages, 3 figures

References in corpus (23)

• Gauge Theory Correlators from Non-Critical String Theory
• AdS/CFT Correspondence and Symmetry Breaking
• Holographic representation of local bulk operators
• Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime
• Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence
• Local bulk operators in AdS/CFT: a boundary view of horizons and locality
• The microlocal spectrum condition and Wick polynomials of free fields on curved spacetimes
• Dynamics in Non-Globally-Hyperbolic Static Spacetimes III: Anti-de Sitter Spacetime
• A universal result on central charges in the presence of double-trace deformations
• Constructing local bulk observables in interacting AdS/CFT
• Local bulk operators in AdS/CFT: A holographic description of the black hole interior
• Double-trace operators and one-loop vacuum energy in AdS/CFT
• Double-Trace Deformations, Mixed Boundary Conditions and Functional Determinants in AdS/CFT
• Boundary-to-bulk maps for AdS causal wedges and the Reeh-Schlieder property in holography
• Intertwining Operator Realization of the AdS/CFT Correspondence
• Null Geodesics, Local CFT Operators and AdS/CFT for Subregions
• CFT representation of interacting bulk gauge fields in AdS
• A smooth introduction to the wavefront set
• Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
• AdS black holes, the bulk-boundary dictionary, and smearing functions
• Ground states of a Klein-Gordon field with Robin boundary conditions in global anti-de Sitter spacetime
• Intertwining Operator Realization of anti de Sitter Holography
• Notes on Relevant, Irrelevant, Marginal and Extremal Double Trace Perturbations

Cited by in corpus (5)

• Bulk reconstruction for spinor fields in AdS/CFT
• HKLL bulk reconstruction for small $\Delta$
• HKLL for the Non-Normalizable Mode
• Extension of the HKLL bulk reconstruction for small $\Delta$
• CFT reconstruction of local bulk operators in half-Minkowski space