Warped Strings: Self-dual Flux and Contemporary Compactifications

TL;DR

<3-5 sentence high-level summary>

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.

Figures (7)

• Figure 1: The electric BPS charges for the two $U(1)$s of equation (\ref{['unbroken']}). F-strings are solid lines, D-strings are dashed. The first $U(1)$ is the torus depicted to the left and the second to the right. The arrows show the string orientations.
• Figure 2: Lattice of coefficients $C_{m,n}$. For $f_2=2$, $f_1=-3$, the independent coefficients are those that lie inside the fundamental cell. The number of BPS states in this case is $13=f^2$.
• Figure 3: The lattice points inside the unit cell for the same case as in figure \ref{['f:fund']}; numbered points are identified under the orientifold reflection followed by lattice translations (equivalent to identifying point related by a reflection with respect to the center of the lattice).
• Figure 4: The possible dS vacua with $V_0$ for given $M$ illustrate the density of states consistent with a discretuum.
• Figure 5: Top:$p$$\overline{\textnormal{D3}}$-branes polarize into an NS5-brane wrapping an $S^2$ on the $A$ cycle. The NS5-brane then slides to the opposite pole, becoming $M-p$ D3-branes. Bottom: In the thin-wall limit, the NS5-brane is instead wraps the $A$ cycle at a particular Euclidean radius.