Statistical Predictions From Anarchic Field Theory Landscapes

TL;DR

This paper explores how statistical methods can predict properties of field theories within constrained landscapes, revealing typical structures and gauge group distributions in theories compatible with quantum gravity.

Contribution

It introduces a coarse-grained statistical framework to predict features of field theories in bounded landscapes, focusing on gauge group distributions and typical structures.

Findings

Predicts high energy theories with many gauge factors.

Shows localization near theories with specific structures.

Indicates decoupling of high and low rank gauge factors.

Abstract

Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness constraints. We argue that appropriately "coarse-grained" aspects of the randomly chosen field theory in such landscapes, such as the fraction of gauge groups with ranks in a given range, can be statistically predictable. To illustrate our point we show how the uniform measures on simple classes of N=1 quiver gauge theories localize in the vicinity of theories with certain typical structures. Generically, this approach would predict a high energy theory with very many gauge factors, with the high rank factors largely decoupled from the low rank factors if we require asymptotic freedom for the latter.