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Flux Compactification

Michael R. Douglas, Shamit Kachru

TL;DR

Flux compactifications stabilize all moduli by turning on fluxes and using dualities to compute a controlled effective potential. This framework yields a vast landscape of metastable vacua with varying cosmological constants, enabling anthropic explanations for the small observed Λ and motivating statistical analyses of vacua distributions. The review covers explicit IIb/IIa constructions, their 4d effective descriptions, and the role of warping and nonperturbative effects in achieving moduli stabilization and SUSY breaking. It highlights observationally relevant avenues in early-universe cosmology and particle phenomenology while acknowledging foundational issues around measure, realism, and the completeness of EFT in quantum gravity.

Abstract

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.

Flux Compactification

TL;DR

Flux compactifications stabilize all moduli by turning on fluxes and using dualities to compute a controlled effective potential. This framework yields a vast landscape of metastable vacua with varying cosmological constants, enabling anthropic explanations for the small observed Λ and motivating statistical analyses of vacua distributions. The review covers explicit IIb/IIa constructions, their 4d effective descriptions, and the role of warping and nonperturbative effects in achieving moduli stabilization and SUSY breaking. It highlights observationally relevant avenues in early-universe cosmology and particle phenomenology while acknowledging foundational issues around measure, realism, and the completeness of EFT in quantum gravity.

Abstract

We review recent work in which compactifications of string and M theory are constructed in which all scalar fields (moduli) are massive, and supersymmetry is broken with a small positive cosmological constant, features needed to reproduce real world physics. We explain how this work implies that there is a ``landscape'' of string/M theory vacua, perhaps containing many candidates for describing real world physics, and present the arguments for and against this idea. We discuss statistical surveys of the landscape, and the prospects for testable consequences of this picture, such as observable effects of moduli, constraints on early cosmology, and predictions for the scale of supersymmetry breaking.

Paper Structure

This paper contains 71 sections, 213 equations, 3 figures.

Table of Contents

  1. INTRODUCTION
  2. A QUALITATIVE PICTURE
  3. Overview of string and M theory compactification
  4. Supersymmetry
  5. Heterotic string
  6. Brane models
  7. Moduli fields
  8. Calabi-Yau manifolds and moduli spaces
  9. Examples
  10. Moduli space - general properties
  11. Flux compactification: Qualitative overview
  12. Freund-Rubin compactification
  13. A solution of the cosmological constant problem
  14. Anthropic selection
  15. Other physical consequences
  16. ...and 56 more sections

Figures (3)

  • Figure 1: Values of $\tau$ for rigid CY flux vacua with $L_{max} = 150$. From Denef:2004ze.
  • Figure 2: The susy vacuum number density per unit $\psi$ coordinate volume, on the real $\psi$-axis, for the mirror quintic. From Denef:2004ze.
  • Figure 3: The toric hypersurfaces with $\chi\ge 0$, from Kreuzer:2000xy. The vertical axis is $h^{1,1}+h^{2,1}$, while the horizontal axis is $\chi=2(h^{1,1}-h^{2,1})$. The full set also contains the mirror manifolds obtained from these by taking $\chi\rightarrow -\chi$.