[Paper Review] Warped Strings: Self-dual Flux and Contemporary Compactifications

Andrew R. Frey|ArXiv.org|Aug 22, 2003

Cosmology and Gravitation TheoriesPhysics and Astronomy228 references20 citations

TL;DR

This dissertation investigates type IIB string compactifications with self-dual fluxes in the internal manifold, showing how fluxes generate a scalar potential that fixes moduli and stabilizes de Sitter vacua. By incorporating nonperturbative effects like D-brane instantons and brane motion, the work provides a mechanism for cosmological evolution, including bounce and decay processes, offering a framework for realizing metastable de Sitter spacetimes in string theory.

ABSTRACT

I review type IIB string compactifications in which the three-form field strengths satisfy a self-duality condition on the internal manifold. I begin with an overview of the models, giving preliminary formulae and several points of view from which they can be understood. Then I describe windows into the small radius behavior of the compactifications, which is more complicated than compactifications without fluxes. I discuss details of the flux-generated potential and nonperturbative corrections to it. These nonperturbative corrections allow a discussion of the cosmological constant and possible mechanisms for the universe to decay from one energy state to another. I conclude with comments on related topics and interesting directions for future study. As this review is a PhD dissertation, I will indicate my own contributions to the subject. However, it is my hope that this document will be a useful and relatively comprehensive review, especially to graduate students. In particular, the early part of the document is almost entirely a literature review.

Motivation & Objective

• To understand the structure and dynamics of type IIB string compactifications with self-dual three-form fluxes on the internal manifold.
• To analyze the scalar potential generated by fluxes and its role in fixing complex structure and dilaton moduli.
• To investigate nonperturbative corrections—such as D-brane instantons and brane motion—that stabilize the cosmological constant and enable decay between vacua.
• To explore the small-radius regime of compactifications, particularly in the presence of fluxes, and its implications for moduli spaces and BPS states.
• To construct viable models of metastable de Sitter spacetimes in string theory using flux and brane dynamics.

Proposed method

• Derives the effective 4D supergravity action from dimensional reduction of type IIB supergravity with fluxes, including warp factors and nontrivial geometry.
• Constructs a flux superpotential and Kähler potential that generate a no-scale potential, enabling moduli stabilization via flux-induced F-terms.
• Analyzes the small-volume regime using moduli space geometry, identifying N=3 and N=4 structures and comparing them to heterotic duals.
• Incorporates nonperturbative effects such as D-instantons and NS5-brane instantons to correct the scalar potential and allow for cosmological transitions.
• Models cosmological evolution via brane motion in throats, including bounce scenarios on conifolds and decay processes involving D7/D3-branes.
• Applies T-duality and $α'$ corrections to analyze photon and D-string moduli dynamics, particularly in asymmetrically warped backgrounds.

Experimental results

Research questions

• RQ1 How do self-dual fluxes in the internal manifold of type IIB compactifications generate a scalar potential that stabilizes moduli?
• RQ2 What is the role of nonperturbative effects—such as D-brane instantons and brane motion—in stabilizing the cosmological constant and enabling transitions between vacua?
• RQ3 How does the small-radius behavior of flux compactifications differ from standard compactifications without fluxes, particularly in terms of moduli space structure?
• RQ4 Can metastable de Sitter vacua be constructed in string theory using fluxes and brane dynamics, and what are their decay mechanisms?
• RQ5 How do dualities such as T-duality and U-duality constrain the dynamics of moduli and the spectrum of BPS states in flux compactifications?

Key findings

• The flux superpotential generates a scalar potential that fixes complex structure moduli and the dilaton, leading to a no-scale structure in the effective 4D theory.
• Nonperturbative corrections from D-instantons and NS5-brane instantons stabilize the potential and allow for cosmological evolution, including bounce and decay processes.
• A metastable de Sitter vacuum can be constructed by combining fluxes with anti-D3 branes, with decay times estimated in Table 4.2 for various decay modes.
• The small-volume regime exhibits rich structure: the moduli space for N=3 theories is identified and compared to N=4 heterotic duals, revealing new dualities.
• T-duality applied to D2-brane and D3-brane systems confirms the consistency of photon and D-string moduli dynamics, with corrected kinetic terms derived at $α'$ order.
• The analysis of brane motion in throats reveals a big bounce scenario on a conifold, suggesting a non-singular cosmological evolution in flux compactifications.