Dimensional regularization for holographic RG flows

Authors: Adam Bzowski and Marjorie Schillo Preprint Number: UUITP-20/19 Abstract: In this work, we present a holographic renormalization scheme for asymptotically anti-de Sitter spacetimes in which the dual renormalization scheme of the boundaryfield theory is dimensional regularization. This constitutes a new level of precision in theholographic 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 ofmotion along renormalization group flows, resolving a long-standing puzzle regarding theWilsonian coupling in holography. This identification of the source field also provides newinsight into field theories deformed by marginal operators, which have been traditionallydifficult 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 conformalanomalies, and conjecture that the conformal anomaly should vanish in the UV for allholographic constructions