A Calculable Toy Model of the Landscape

TL;DR

This paper introduces a calculable, field-theoretic toy model mimicking the string landscape with multiple vacua, enabling explicit calculations of physical properties and illustrating landscape evolution with energy.

Contribution

It presents a novel, explicit model with rich vacuum structure, incorporating supergravity effects, to study landscape dynamics and vacuum stability in a simplified setting.

Findings

Rich vacuum structure with different stable classes

Explicit calculation of supersymmetry-breaking scales

Demonstration of landscape evolution and phase transitions

Abstract

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. We also demonstrate that supergravity effects are crucial in order to stabilize most of these vacua, and in order to allow the possibility of cancelling the cosmological constant.