[Paper Review] A Tutorial on Links between Cosmic String Theory and Superstring Theory

Mahbub Majumdar|ArXiv.org|Dec 6, 2005

Black Holes and Theoretical Physics73 references3 citations

TL;DR

This tutorial bridges cosmic string theory and superstring theory by explaining how tachyon condensation and warped compactifications can produce stable, long cosmic superstrings—particularly (p,q) strings—whose low tension makes them cosmologically viable. It derives their intercommutation probability P<1, shows how this leads to scaling network dynamics, and calculates gravitational wave emission from cusps, offering a detectable signature for string theory in the early universe.

ABSTRACT

Cosmic superstrings are introduced to non-experts. First D-branes and $(p,q)$ strings are discussed. Then we explain how tachyon condensation in the early universe may have produced F, D and $(p,q)$ strings. Warped geometries which can render horizon sized superstrings relatively light are discussed. Various warped geometries including the deformed conifold in the Klebanov-Strassler geometry are reviewed and their warp factors are calculated. The decay rates for strings in the KS geometry are calculated and reasons for the necessity of orientifolds are reviewed. We then outline calculations of the intercommuting probability of F, D and $(p,q)$ strings and explain in detail why cosmic superstring intercommuting probabilities can be small. We explore cosmic superstring networks. Their scaling properties are examined using the Velocity One Scale model and its extra dimensional extensions. Two different approaches and two sets of simulations are reviewed. Finally, we review in detail the gravitational wave amplitude calculations for strings with intercommuting probability $P&lt;1$.

Motivation & Objective

• To establish a conceptual and technical bridge between cosmic string theory and superstring theory for non-experts.
• To explain how tachyon condensation and warped geometries can produce stable, long cosmic superstrings with low tension.
• To analyze the intercommuting probability P<1 for F, D, and (p,q) strings and its impact on network scaling.
• To derive gravitational wave amplitudes from cusps on cosmic superstrings with P<1, enabling observational tests.
• To address foundational issues such as orientifold necessity, string stability, and the role of moduli in cosmological models.

Proposed method

• Uses D-branes and (p,q) string theory to describe extended objects in extra dimensions and their solitonic nature.
• Applies tachyon condensation in boundary CFT to model F-string creation during phase transitions.
• Calculates warp factors in warped geometries, including the deformed conifold in Klebanov-Strassler, to suppress string tension.
• Analyzes intercommutation probabilities via string scattering and 2D SYM toy models, showing P<1 due to non-perturbative effects.
• Employs the Velocity One Scale (VOS) model and its D-dimensional extensions to simulate network scaling with P<1.
• Derives gravitational wave amplitudes from cusp formation on strings, assuming no backreaction and power-law decay.

Experimental results

Research questions

• RQ1 How can tachyon condensation in the early universe produce F, D, and (p,q) strings relevant to cosmic superstrings?
• RQ2 What role do warped geometries—especially the deformed conifold—play in making superstrings cosmologically viable by reducing their tension?
• RQ3 Why is the intercommuting probability P<1 for F and D strings, and how does this affect the scaling behavior of cosmic superstring networks?
• RQ4 How do gravitational wave signals from cusps on cosmic superstrings with P<1 differ from standard cosmic string predictions?
• RQ5 What are the implications of orientifolds and fermion zero modes for the stability and longevity of cosmic superstring loops?

Key findings

• Warped geometries such as the deformed conifold in the Klebanov-Strassler setup can reduce string tension to cosmologically viable levels, making long superstrings observable.
• The intercommuting probability for F and D strings is less than one due to non-perturbative stringy effects, with P≈0.1–0.3 in some models, leading to non-standard network scaling.
• Scaling of cosmic superstring networks is governed by γ∼P^{1/3} or similar fractional power, deviating from the √P scaling expected from simple correlation length arguments.
• Gravitational wave emission from cusps on strings with P<1 produces a power-law spectrum h(f)∝f^{-1/3}, though backreaction may alter this to exponential decay in full quantum treatments.
• Stable, non-BPS (p,q) strings can exist in orientifolded compactifications, and their formation is linked to tachyonic phase transitions in brane-antibrane systems.
• Numerical simulations suggest that (p,q) string networks can scale, but the timescale to reach scaling may be long, affecting observational relevance.