Exponentially Large Extra Dimensions

TL;DR

This work presents a mechanism to generate exponentially large extra dimensions by leveraging a very light six-dimensional scalar with a cubic self-interaction, which induces a logarithmic radion potential through radiative corrections. Renormalization-group running of the dimensionless coupling $g$ yields a potential $V(r)$ that stabilizes at a radius $r$ exponentially larger than the microscopic scale $\ell$, with a radion mass $m \sim 1/(M_p r^2)$ that remains technically natural. The authors compute the one- and two-loop Casimir energies, analyze the conditions under which the stationary radius is exponentially large, and discuss the phenomenological implications, including cosmological evolution of the radion couplings, potential quintessence behavior, and collider signatures. While constructing fully natural microscopic models remains challenging, the scenario offers a concrete route to drastically large extra dimensions and distinctive cosmological/gravitational phenomenology constrained by current experiments.

Abstract

We show how the presence of a very light scalar with a cubic self-interaction in six dimensions can stabilize the extra dimensions at radii which are naturally exponentially large, $r \sim \ell \exp [(4π)^3/g^2]$, where $\ell$ is a microscopic physics scale and $g$ is the (dimensionless) cubic coupling constant. The resulting radion mode of the metric becomes a very light degree of freedom whose mass, $m \sim 1/(M_p r^2)$ is stable under radiative corrections. For $1/r \sim 10^{-3}$ eV the radion is extremely light, $m \sim 10^{-33}$ eV. Its couplings cause important deviations from General Relativity in the very early universe, but naturally evolve to phenomenologically acceptable values at present.