Randomness-assisted exponential hierarchies

Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular, we find a new class of nonlocal theory space models, in which scalar fields at nonadjacent sites interact with each other but with strengths decaying exponentially with the site separation. Such a model could have very different localization properties, compared to the local theory space scenarios with only nearest-site interactions, based on the original Anderson localization model. More specifically, we find that a particular nonlocal interaction pattern leads to bilocalization of the two lightest eigenstates. Exponential localization (and thus exponentially suppressed couplings) then emerges only and immediately when randomness is introduced, no matter how tiny it is. We discuss variants of the model and possible UV completions as well.

Automated summary

Inspired by localization phenomenon in condensed matter systems, the study explores constructions in the theory space of multiple scalar fields, where exponentially suppressed couplings could originate from random parameters. A new class of nonlocal theory space models is found, in which scalar fields at nonadjacent sites interact with strengths decaying exponentially with separation. Such models exhibit different localization properties compared to local scenarios, with bilocalization of the two lightest eigenstates observed under specific nonlocal interaction pattern. Exponential localization and suppressed couplings emerge immediately upon introducing randomness, regardless of its magnitude. Variants of the model and possible UV completions are also discussed.