[Paper Review] Gravity and strings

Steven B. Giddings|ArXiv.org|Jan 11, 2005

Cosmology and Gravitation Theories10 references3 citations

TL;DR

This paper reviews how string theory resolves the non-renormalizability of quantum gravity by providing an ultraviolet-finite framework, predicts gauge theories and fermions, and addresses the cosmological constant and hierarchy problems through moduli stabilization via fluxes and branes. A key result is the prediction of a metastable universe undergoing spontaneous decompactification of extra dimensions, leading to ultimate decay via bubble nucleation on timescales of order exp(10^120).

ABSTRACT

This is a broad-brush review of how string theory addresses several important questions of gravitational physics. The problem of non-renormalizability is first reviewed, followed by introduction of string theory as an ultraviolet-finite theory of gravity. String theory's successes also include predicting both gauge theory and fermions. The difficulty of extra dimensions becomes a possible virtue, when one notes that these lead to mechanisms to explain fermion generations, as well as a means to break the large gauge symmetries of string theory. Finally, a long standing problem of string theory, that of fixing the size and shape of the extra dimensions, has recently been addressed and may shed light on the origin of the cosmological constant, the ultimate fate of our universe, as well as the question of why gravity_is_ so weak.

Motivation & Objective

• To address the non-renormalizability of quantum gravity in effective field theory by showing how string theory provides a UV-finite alternative.
• To explain how string theory naturally incorporates gauge symmetries, fermions, and the structure of matter generations through extra dimensions.
• To investigate the mechanism for fixing the size and shape of extra dimensions (the moduli problem) and its implications for dark energy and the cosmological constant.
• To explore the cosmological fate of our universe within string theory, particularly the instability of four-dimensional de Sitter space due to spontaneous decompactification of extra dimensions.
• To examine the anthropic landscape of string vacua and the role of flux compactifications in fixing the observed value of the cosmological constant.

Proposed method

• Uses effective field theory and dimensional analysis to show that quantum gravity amplitudes diverge at high energies due to the negative mass dimension of Newton's constant.
• Applies string theory's extended object structure (strings) to replace point particles, thereby eliminating ultraviolet divergences and providing a finite quantum gravity framework.
• Analyzes compactifications with fluxes and branes to stabilize moduli, using the superpotential and F-term potential to generate a scalar potential for moduli fields.
• Applies the no-scale structure and non-perturbative effects (e.g., D-instantons) to stabilize the remaining modulus in type IIB compactifications.
• Constructs explicit models with anti-D3 branes to generate a positive cosmological constant, consistent with observations.
• Evaluates the stability of four-dimensional de Sitter vacua by analyzing the potential for extra-dimensional volume moduli, showing a generic tendency toward decompactification.

Experimental results

Research questions

• RQ1 How does string theory resolve the non-renormalizability of quantum gravity, and what makes it UV-finite compared to effective field theory?
• RQ2 What mechanisms in string compactifications can stabilize the size and shape of extra dimensions, and how do fluxes and branes contribute to this?
• RQ3 How does the stabilization of moduli lead to a prediction of the observed value of the cosmological constant?
• RQ4 What is the ultimate fate of our universe in string theory, particularly in the context of de Sitter space and extra-dimensional decompactification?
• RQ5 Can the anthropic principle, combined with the landscape of string vacua, explain the small observed value of the cosmological constant?

Key findings

• String theory provides a UV-finite quantum gravity framework by replacing point particles with extended strings, eliminating the divergences that plague effective field theory.
• The theory naturally incorporates gauge symmetries and fermions through the structure of string compactifications and worldsheet conformal field theory.
• Moduli stabilization via fluxes and branes generates a scalar potential that fixes the size and shape of extra dimensions, leading to a prediction of dark energy with a small cosmological constant.
• The presence of anti-D3 branes in type IIB compactifications allows for the construction of metastable de Sitter vacua with positive cosmological constant, consistent with observation.
• The four-dimensional universe is generically unstable to spontaneous decompactification of extra dimensions, leading to a bubble nucleation process that would ultimately consume the observable universe on a timescale of exp(10^120).
• The landscape of string vacua, combined with flux compactifications, provides a framework where the cosmological constant is fixed by anthropic selection, explaining its small observed value.