# Dimensional regularization for holographic RG flows

## TL;DR

This paper introduces a holographic renormalization scheme using dimensional regularization for AdS spacetimes, enabling precise matching of scheme-dependent quantities and resolving longstanding puzzles about Wilsonian couplings in holography.

## Contribution

It develops a new holographic renormalization method based on dimensional regularization, improving the holographic dictionary and clarifying the role of source fields in RG flows.

## Key findings

- Exact matching of holographic and field theory beta functions
- Identification of a local source field satisfying RG flow equations
- Relation between beta function analyticity and absence of conformal anomalies

## 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.