[Paper Review] SUSY Breaking, Cosmology, Vacuum Selection and the Cosmological Constant in String Theory

T. Banks|ArXiv.org|Jan 26, 1996

Cosmology and Gravitation Theories2 references24 citations

TL;DR

This paper proposes that cosmological constraints—particularly the requirement for a viable inflationary scenario and a vanishing cosmological constant—select the correct vacuum in string theory, favoring hidden-sector supersymmetry (SUSY) breaking over low-energy SUSY breaking. It argues that hidden-sector SUSY breaking naturally stabilizes the dilaton and yields a cosmological constant near the observational bound, while low-energy SUSY breaking leads to cosmologically problematic light dilatons and coherent forces.

ABSTRACT

This is the written version of a talk given at the Santa Barbara Workshop on Supersymmetry in December of 1995. It summarizes a collection of results on superstring cosmology obtained by the author and various collaborators, and contains some speculations about the resolution of the cosmological constant and vacuum selection problems in string theory.

Motivation & Objective

• To identify the physical principles that select the correct vacuum state in string theory, arguing that cosmology—not just field theory—is essential.
• To resolve the Dine-Seiberg problem of the runaway dilaton by showing that nonperturbative corrections to the Kähler potential can stabilize it in weakly coupled regimes.
• To explain why four large spacetime dimensions and broken supersymmetry are likely outcomes of cosmological selection principles.
• To assess the viability of low-energy SUSY breaking in string theory, highlighting its cosmological problems due to light dilatons.
• To estimate the cosmological constant using holographic principles, with results dependent on the SUSY breaking mechanism.

Proposed method

• Uses effective field theory of superstrings (EFTS) with weak coupling near the string scale as a foundational assumption.
• Applies analyticity and S-duality constraints to argue that the dilaton superpotential is dominated by a pure exponential, with nonperturbative corrections to the Kähler potential enabling stabilization.
• Leverages matrix model and string field theory arguments to estimate nonperturbative corrections of order $e^{-c/g}$, with $c \sim 1$.
• Uses the holographic principle to speculate on cosmological constant estimation, comparing hidden-sector vs. low-energy SUSY breaking scenarios.
• Analyzes the implications of dilaton mass and coupling for cosmological reheating and coherent forces, using experimental bounds on force ranges.
• Applies perturbative and nonperturbative field theory techniques, including Borel transform and conformal mapping, to explore large-order behavior of the Kähler potential expansion.

Experimental results

Research questions

• RQ1 Why does string theory select a vacuum with four large spacetime dimensions and broken supersymmetry?
• RQ2 How can the dilaton be stabilized in weakly coupled string theory despite the Dine-Seiberg runaway problem?
• RQ3 What are the cosmological consequences of low-energy SUSY breaking in string theory, particularly regarding the dilaton?
• RQ4 Can the cosmological constant be estimated using holographic principles in string theory?
• RQ5 Why is hidden-sector SUSY breaking preferred over low-energy SUSY breaking from a cosmological standpoint?

Key findings

• The requirement of a viable inflationary scenario with sufficient e-foldings selects vacua where the cosmological constant is vanishing or near the observational bound.
• Hidden-sector SUSY breaking leads to a cosmological constant estimate close to the current observational bound, while low-energy SUSY breaking yields a value too small to be observationally relevant.
• Low-energy SUSY breaking leads to a very light dilaton, which would mediate coherent forces with millimeter to centimeter range, posing a cosmological reheating problem.
• Nonperturbative corrections to the Kähler potential—possibly of order $e^{-1/g}$—can stabilize the dilaton even when the superpotential remains perturbative.
• The absence of dimension-dependent powers of $4\pi$ in nonperturbative corrections suggests a fundamental difference between string theory and quantum field theory in the origin of expansion parameters.
• The holographic principle, if valid, undermines standard field-theoretic expectations for the naturalness of the cosmological constant, supporting the idea that its small value may be selected by cosmological dynamics.