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

• Main Authors: Nicolás Del Grosso, Alan Garbarz, Gabriel Palau, Guillem Pérez-Nadal
• Format: Article
• Language: English
• Published: SpringerOpen 2019-10-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Renormalization Group; Conformal Field Theory
• Online Access: http://link.springer.com/article/10.1007/JHEP10(2019)135

Abstract We consider the problem of defining spacelike-supported boundary-to-bulk propagators in AdS d+1 down to the unitary bound ∆ = (d − 2)/2. That is to say, we construct the ‘smearing functions’ K of HKLL but with different boundary conditions where both dimensions ∆+ and ∆ − 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.