# Random Polynomials and the Friendly Landscape

@article{Distler2005RandomPA, title={Random Polynomials and the Friendly Landscape}, author={Jacques Distler and Uday Varadarajan}, journal={arXiv: High Energy Physics - Theory}, year={2005} }

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.

#### Paper Mentions

#### 31 Citations

Random Field Theories in The Mirror Quintic Moduli Space

- Physics
- 2016

We investigate the distribution of field theories that arise from the low energy limit of flux vacua built on type IIB string theory compactified on the mirror quintic. For a large collection of… Expand

Calabi-Yau CFTs and Random Matrices

- Physics, Mathematics
- 2021

Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi–Yau targets at large… Expand

Gauge sector statistics of intersecting D-brane models

- Physics
- 2007

In this paper, which is based on the first part of the author's PhD thesis, we review the statistics of the open string sector in T6/(ℤ2 × ℤ2) orientifold compactifications of type IIA. After an… Expand

A new method for finding vacua in string phenomenology

- Physics
- 2007

One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all… Expand

The Swampland: Introduction and Review

- Physics, Chemistry
- Fortschritte der Physik
- 2019

The Swampland program aims to distinguish effective theories which can be completed into quantum gravity in the ultraviolet from those which cannot. This article forms an introduction to the field,… Expand

A Simple Introduction to Gröbner Basis Methods in String Phenomenology

- Physics
- 2009

I give an elementary introduction to the key algorithm used in recent applications
of computational algebraic geometry to the subject of string phenomenology. I
begin with a simple description of… Expand

One in a Billion: MSSM-like D-Brane Statistics

- Physics
- 2006

Continuing our recent work hep-th/0411173, we study the statistics of four-dimensional, supersymmetric intersecting D-brane models in a toroidal orientifold background. We have performed a vast… Expand

Monodromy inflation in SUSY QCD

- Physics
- 2014

A bstractThe discovery of a large tensor-to-scalar ratio by the BICEP2 experiment points to large field excursions during inflation. One framework that predicts large r is monodromy inflation. While… Expand

Statistics on the heterotic landscape: Gauge groups and cosmological constants of four-dimensional heterotic strings

- Physics
- 2006

Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and nonsupersymmetric string vacua fills out a landscape whose features are largely unknown. It… Expand

Random matrices and the spectrum of N-flation

- Physics
- 2006

N-flation is a promising embedding of inflation in string theory in which many string axions combine to drive inflation. We characterize the dynamics of a general N-flation model with nondegenerate… Expand

#### References

SHOWING 1-10 OF 52 REFERENCES

The statistics of string/M theory vacua

- Physics
- 2003

We discuss systematic approaches to the classification of string/M theory vacua, and physical questions this might help us resolve. To this end, we initiate the study of ensembles of effective… Expand

Statistics of string vacua

- Physics
- 2003

In 1975, Scherk and Schwarz proposed that string theory could unify quantum gravity with all other fundamental interactions. This proposal has met with some success, and its study has led to dramatic… Expand

R symmetries in the landscape

- Physics
- 2006

In the landscape, states with R symmetries at the classical level form a distinct branch, with a potentially interesting phenomenology. Some preliminary analyses suggested that the population of… Expand

A Calculable Toy Model of the Landscape

- Physics
- 2004

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… Expand

Basic results in vacuum statistics

- Physics
- 2004

Abstract This is a review of recent work on constructing and finding statistics of string theory vacua, done in collaboration with Frederik Denef, Bogdan Florea, Bernard Shiffman and Steve Zelditch.… Expand

Calculable toy model of the string-theory landscape

- Physics
- 2005

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… Expand

SUPERSYMMETRY, NATURALNESS AND THE LANDSCAPE

- Mathematics, Physics
- 2004

We argue that the study of the statistics of the landscape of string vacua provides the first potentially predictive -- and also falsifiable -- framework for string theory. The question of whether… Expand

The Anthropic Landscape of String Theory

- Physics
- 2003

In this lecture I make some educated guesses, about the landscape of string theory vacua. Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably large… Expand

On the cosmological constant problem

- Physics
- 1984

Abstract We prove that Weyl invariant theories of gravity possess a remarkable property which, under very general assumptions, explains the stability of flat space-time. We show explicitly how… Expand

Counting flux vacua

- Physics
- 2004

We develop a technique for computing expected numbers of vacua in gaussian ensembles of supergravity theories, and apply it to derive an asymptotic formula for the index counting all flux… Expand