Perturbative RG flows in AdS: an \'etude

TL;DR

This paper explores perturbative renormalization group flows in Anti-de Sitter space, emphasizing boundary conditions and covariance, and applies these ideas to minimal models, revealing simpler flow structures than in flat-space boundary QFT.

Contribution

It provides a novel analysis of RG flows in AdS, highlighting boundary condition treatment, covariance properties, and a conjectured simplified flow diagram for minimal models.

Findings

Boundary correlation functions remain conformally covariant despite bulk scale.

RG flow between minimal models can be represented by a simpler diagram in AdS.

Boundary conditions in AdS influence RG flow properties distinctly from flat space.

Abstract

We discuss general properties of perturbative RG flows in AdS with a focus on the treatment of boundary conditions and infrared divergences. In contrast with flat-space boundary QFT, general covariance in AdS implies the absence of independent boundary flows. We illustrate how boundary correlation functions remain conformally covariant even if the bulk QFT has a scale. We apply our general discussion to the RG flow between consecutive unitary diagonal minimal models which is triggered by the $\phi_{(1,3)}$ operator. For these theories we conjecture a flow diagram whose form is significantly simpler than that in flat-space boundary QFT. In several stand-alone appendices we discuss two-dimensional BCFTs in general and the minimal model BCFTs in particular. These include both an extensive review as well as the computation of several new BCFT correlation functions.