Perturbative RG flows in AdS. An étude

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 ϕ(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.

Analytic and numerical bootstrap for the long-range Ising model

“…where we divided by the tree-level result. 8 Since there is no wave-function renormalization for φ, the 1/ε pole in this diagram is removed by a wave-function renormalization for [ φ φ] n,ℓ , which in turn leads to the following scaling dimension for [ φ φ] n,ℓ at the IR fixed point:…”

“…This generalizes the result in [28,50] and also corrects a factor of 2 for the leading twist N = 1 result. 8 As the spinning operator does not carry momentum, derivatives will produce the same effect no matter how they are distributed: they simply contribute the same factor of k…”

“…The importance of studying Conformal Field Theories (CFTs) without a stress tensor can be motivated from various angles. The past decade has seen a surge of interest in Quantum Field Theories (QFTs) that live on a fixed Anti-de Sitter (AdS) background [1][2][3][4][5][6][7][8]. Due to the lack of dynamical gravity, the CFT which encodes boundary correlation functions has…”

A bootstrap study of minimal model deformations

“…In section 3, we make use of the results of [19] to study conformal perturbation theory in AdS at leading order. We derive the modification to boundary CFT data when the bulk is perturbed by a general Virasoro primary or by a special Virasoro descendant of the identity: the T T operator.…”

“…The IR divergences can be cured by including bulk counterterms evaluated at a cut-off surface near the boundary. As discussed for example in [19], these counterterms can generally be chosen to preserve boundary conformal invariance and then the 'boundary follows the bulk'. 3 This is in contrast to flatspace RG flows emanating from BCFTs where bulk and boundary can flow independently, see for instance [39][40][41].…”