Exponential Hierarchies from Anderson Localization in Theory Space

Understand

We present a new mechanism for generating exponential hierarchies in four-dimensional field theories inspired by Anderson localization in one dimension, exploiting an analogy between the localization of electron energy eigenstates along a one-dimensional disordered wire and the localization of mass eigenstates along a local "theory space" with random mass parameters.

• Mass eigenstates are localized even at arbitrarily weak disorder, with exponentially suppressed couplings to sites in the theory space.
• The mechanism is quite general and may be used to exponentially localize fields of any spin.
• We apply the localization mechanism to two hierarchies in Standard Model parameters --- the smallness of neutrino masses and the ordering of quark masses --- and comment on possible relevance to the electroweak hierarchy problem.