Random Polynomials and the Friendly Landscape

TL;DR

This paper extends a toy model of the string theory landscape to realistic effective Lagrangians, using advanced algebraic geometry to analyze the multitude of metastable vacua.

Contribution

It demonstrates that the toy model considerations apply to realistic string-derived Lagrangians and reviews the algebraic geometry methods needed for analyzing metastable vacua.

Findings

Applicability of toy model considerations to realistic Lagrangians

Development of algebraic geometry techniques for vacuum analysis

Insights into the structure of metastable vacua in string theory

Abstract

In hep-th/0501082, a field theoretic ``toy model'' for the Landscape was proposed. We show that the considerations of that paper carry through to realistic effective Lagrangians, such as those that emerge out of string theory. Extracting the physics of the large number of metastable vacua that ensue requires somewhat more sophisticated algebro-geometric techniques, which we review.