Dynamical Constraints on RG Flows and Cosmology

TL;DR

Sets the goal of constraining cosmological EFTs by importing rigorous bounds from AdS/CFT via slow holographic RG flows. Develops a DIS-based sum rule that ties the bulk radial infall speed c_r to a boundary four-point function, deriving a spin-2 anomalous-dimension constraint γ_2 and showing γ_2≤0; in the c_r→1 limit, bulk EFTs are forced to be free due to causality. Extends the framework to connect with inflation, noting analogous structures for c_s and potential positivity constraints, and discusses the DBI case as a concrete example. The work provides a principled bridge between RG-flow dynamics and inflationary phenomenology, offering a roadmap for translating UV consistency requirements into inflationary model-building and vice versa.

Abstract

Sum rules connecting low-energy observables to high-energy physics are an interesting way to probe the mechanism of inflation and its ultraviolet origin. Unfortunately, such sum rules have proven difficult to study in a cosmological setting. Motivated by this problem, we investigate a precise analogue of inflation in anti-de Sitter spacetime, where it becomes dual to a slow renormalization group flow in the boundary quantum field theory. This dual description provides a firm footing for exploring the constraints of unitarity, analyticity, and causality on the bulk effective field theory. We derive a sum rule that constrains the bulk coupling constants in this theory. In the bulk, the sum rule is related to the speed of radial propagation, while on the boundary, it governs the spreading of nonlocal operators. When the spreading speed approaches the speed of light, the sum rule is saturated, suggesting that the theory becomes free in this limit. We also discuss whether similar results apply to inflation, where an analogous sum rule exists for the propagation speed of inflationary fluctuations.

Figures (6)

• Figure 1: During inflation ( left), the time dependence of a matter field $\phi(\eta)$ induces a preferred time slicing of the quasi-de Sitter background. The analog in AdS is a slow RG flow ( right) induced by the radial profile $\phi(z)$ of a bulk field. In both cases, the low-energy dynamics can be described by Goldstone fluctuations around the homogeneous background.
• Figure 2: Illustration of the growth of an operator in the vacuum state of a QFT for a generic RG flow ( left) and the slow RG flow ( right). The operator $W$ is smeared within a small region near the origin. As the operator spreads in space, it probes larger scales, and effectively transitions from the UV CFT at early times to the IR CFT at late times. The growth curve $R(t)$ depends on the UV operator and the details of the RG flow. In the slow RG limit, the operator grows linearly over a large range of scales. The speed of operator growth ${\rm d} R/dt$ is then equal to the AdS infall speed $c_r$.
• Figure 3: Illustration of deep inelastic scattering ( left) and the DIS amplitude ( right).
• Figure 4: Illustration of the analytic structure of the DIS amplitude.
• Figure 5: Witten diagrams associated with the contact interaction $( \partial \pi_c)^4$ and the exchange interactions arising from $\partial_r \pi_c(\partial \pi_c)^2$ and $(\partial_r \pi_c)^3$.