Abstract
In this work, we present a holographic renormalization scheme for asymptotically anti-de Sitter spacetimes in which the dual renormalization scheme of the boundary field theory is dimensional regularization. This constitutes a new level of precision in the holographic dictionary and paves the way for the exact matching of scheme dependent quantities, such as holographic beta functions, with field theory computations. Furthermore, the renormalization procedure identifies a local source field which satisfies the equations of motion along renormalization group flows, resolving a long-standing puzzle regarding the Wilsonian coupling in holography. This identification of the source field also provides new insight into field theories deformed by marginal operators, which have been traditionally difficult to analyze due to altered bulk asymptotics. Finally, we demonstrate a new relation equating the analyticity of the holographic beta function to the absence of conformal anomalies, and conjecture that the conformal anomaly should vanish in the UV for all holographic constructions.
Highlights
In the UV CFT, it was argued in [4] that the value of the field at a given radial position should correspond to the value of the coupling at this scale
In this work, we present a holographic renormalization scheme for asymptotically anti-de Sitter spacetimes in which the dual renormalization scheme of the boundary field theory is dimensional regularization
In this paper we have presented the first instance of a bulk holographic renomalization scheme which corresponds to a know field theory renormalization scheme: dimensional renormalization
Summary
The original application of the AdS/CFT correspondence, and the one we will pursue here, is to use a weakly coupled gravitational system in an asymptotically AdS spacetime to define a dual QFT non-perturbatively. The radial or near-boundary expansion of the scalar field Φ is given by: κΦ = φ(d−∆)zd−∆ + . For d/2 < ∆ < d the leading behavior of the scalar field is given by κΦ ∼ φ(d−∆)zd−∆. The AdS/CFT correspondence states that there exists a one-to-one map between single trace conformal primaries in the boundary CFT (which is the UV fixed point of the boundary QFT) and bulk fields in the gravity dual. Where φ(d−∆), the asymptotic boundary value of the bulk field Φ, is identified as the source of the corresponding operator, O∆, on the field theory side. On-shell bulk action should be well defined; this requires holographic renormalization to regulate divergences in the on-shell action, e.g. due to the infinite volume of AdS
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