Dynamical Constraints on RG Flows and Cosmology. (arXiv:1906.10226v1 [hep-th])
<a href="http://arxiv.org/find/hep-th/1/au:+Baumann_D/0/1/0/all/0/1">Daniel Baumann</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Green_D/0/1/0/all/0/1">Daniel Green</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Hartman_T/0/1/0/all/0/1">Thomas Hartman</a>
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.
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.
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