[Paper Review] NS-branes in 5d brane world models

Eunkyung Park, Pyung Seong Kwon|arXiv (Cornell University)|Jul 8, 2010

Black Holes and Theoretical Physics32 references3 citations

TL;DR

This paper argues that in 5D brane world models compactified on $S^1/\mathbb{Z}_2$, background NS-branes—rather than D-branes—are essential to achieve a flat geometry $M_4 \times S^1/\mathbb{Z}_2$; without them, the 5D metric becomes singular. The result parallels a similar mechanism in $(p+3)$D effective string theory, suggesting NS-branes may underlie the true background geometry of spacetime, offering a potential resolution to the cosmological constant problem via a self-tuning mechanism.

ABSTRACT

We study codimension-1 brane solutions of the 5d brane world models compactified on $S_1 / \mathbb{Z}_2$. In string theoretical setup they suggest that the background branes located at orbifold fixed points should be NS-branes (in the five dimensional sense), rather than D-branes. Indeed, the existence of the background NS-branes is indispensable to obtain flat geometry $M_4 imes S_1 / \mathbb{Z}_2$ where $M_4$ represents the 4d Minkowski spacetime, and without these branes the 5d metric becomes singular everywhere. This result is very reminiscent of the $(p+3)$d effective string theory \cite{1} where the NS-NS type $p$-brane is indispensable to obtain a flat geometry $R_2$ or $R_2 /\mathbb{Z}_n$ on the transverse dimensions. Without this NS-NS type $p$-brane the 2d transverse space becomes a pin-shaped singular space. The correspondence between these two theories leads us to a conjecture that the whole flat backgrounds of the string theory inherently invovle the NS-branes implicitly in their ansatz, and hence the true background $p$-branes immanent in our spacetime may be NS-branes, instead of D-branes. We argue that this result can have a significant consequence in the context of the cosmological constant problem.

Motivation & Objective

• To investigate the role of NS-branes in 5D brane world models compactified on $S^1/\mathbb{Z}_2$.
• To determine whether NS-branes are necessary for achieving a flat 5D geometry $M_4 \times S^1/\mathbb{Z}_2$.
• To explore the implications of NS-brane backgrounds for the cosmological constant problem.
• To establish a correspondence between 5D brane world models and $(p+3)$D effective string theory in terms of NS-brane necessity.

Proposed method

• Formulate a 5D gravity-scalar action with a scalar field $\phi$ and a cosmological term $\lambda$ in the bulk.
• Include brane actions with tensions $T^{(i)}(\phi) = T^{(i)}_0 e^{\alpha\phi}$ at orbifold fixed points.
• Analyze codimension-1 brane solutions in the string-theoretic setup, identifying the background branes as NS-branes.
• Compare the 5D model with $(p+3)$D effective string theory, where NS-NS $p$-branes are required for flat transverse geometry.
• Use the correspondence to argue that NS-branes are implicitly present in flat string backgrounds.
• Estimate the string scale $M_s$, 5D Planck scale $M_5$, and compactification radius $R_c$ to assess consistency with the hierarchy problem.

Experimental results

Research questions

• RQ1 Why is the presence of background NS-branes necessary to achieve a flat $M_4 \times S^1/\mathbb{Z}_2$ geometry in 5D brane world models?
• RQ2 How does the requirement of NS-branes in 5D models compare to their role in $(p+3)$D effective string theory?
• RQ3 Can the cosmological constant problem be resolved through a self-tuning mechanism involving background NS-branes?
• RQ4 What is the relationship between the 5D Planck scale $M_5$, string scale $M_s$, and compactification radius $R_c$ in the presence of NS-branes?
• RQ5 Is the string theoretical interpretation of the model viable when $\lambda \neq 0$, and what does this imply for coupling constants?

Key findings

• NS-branes are indispensable for achieving a flat 5D geometry $M_4 \times S^1/\mathbb{Z}_2$; without them, the metric becomes singular everywhere.
• The 5D model mirrors the $(p+3)$D string theory case, where NS-NS $p$-branes are required to avoid singular transverse geometry.
• The existence of background NS-branes suppresses quantum fluctuations of SM fields, enabling a self-tuning mechanism for the cosmological constant.
• In the limit $g_s \to 0$, quantum corrections to the compactification scale and coupling constants are highly suppressed.
• The 4D Planck scale satisfies $M_{\text{pl}}^2 \sim M_5^3 R_c / g_s^2$, which allows $M_5 \sim \text{TeV}$ and $R_c \sim \text{TeV}^{-1}$ with $g_s \sim 10^{-16}$, consistent with the hierarchy assumption.
• When $M_5 \sim M_s \sim \text{TeV}$, the condition $\sqrt{-\lambda} R_c \sim O(1)$ leads to $g_s \sim 10^{-16}$, matching the decoupling limit of Little String Theory.