A calculable field-theoretic "landscape": Vacuum structure, phase transitions, and infrared fixed points

Motivated by recent discussions of the string-theory landscape, we propose field-theoretic realizations of models with large numbers of vacua. These models contain multiple U(1) gauge groups, and can be interpreted as deconstructed versions of higher-dimensional gauge theory models with fluxes in the compact space. We find that the vacuum structure of these models is very rich, defined by parameter-space regions with different classes of stable vacua separated by boundaries. This allows us to explicitly calculate physical quantities such as the supersymmetry-breaking scale, the presence or absence of R-symmetries, and probabilities of stable versus unstable vacua. Furthermore, we find that this landscape picture evolves with energy, allowing vacua to undergo phase transitions as they cross the boundaries between different regions in the landscape. Surprisingly, we show that this landscape flow approaches an infrared fixed point, suggesting that it may not be necessary to determine all of the parameters of the ultraviolet theory in order to deduce relevant features of the low-energy phenomenology.