Avoiding an Empty Universe in RS I Models and Large-N Gauge Theories
Jared Kaplan, Philip C. Schuster, Natalia Toro
TL;DR
The paper analyzes why confinement transitions in RS-I and large-$N$ gauge theories are parametrically slow, risking an empty universe after inflation due to a transition rate $\Gamma \sim \Lambda^4 e^{-cN^2}$ and $H \sim N\Lambda^2/M_{pl}$. It links this suppression to approximate conformal symmetry and explores a path to faster transitions if the radion potential is asymptotically free, allowing an instanton to proceed with action $S \sim N^2$ even near the Landau pole. The work also identifies TeV-scale magnetic monopoles, potentially produced during the phase transition, as distinctive signatures. Overall, it argues that viable models require modest $N$ (roughly $N\lesssim 10$–12) and outlines observational probes, including monopole searches, to test the scenario.
Abstract
Many proposed solutions to the hierarchy problem rely on dimensional transmutation in asymptotically free gauge theories, and these theories often have dual descriptions in terms of a warped extra dimension. Gravitational calculations show that the confining phase transition in Randall-Sundrum models is first-order and parametrically slower than the rate expected in large-N gauge theories. This is dangerous because it leads to an empty universe problem. We argue that this rate suppression arises from approximate conformal symmetry. Though this empty universe problem cannot be solved by using the radion for low-scale inflation, we argue that if the radion potential is asymptotically free, another instanton for the RS phase transition can proceed as $e^{-N^2}$. We also discuss the existence of light magnetic monopoles ($\sim 100$ TeV) as a possible signature of such a phase transition.