Stabilization of Extra Dimensions and The Dimensionality of the Observed Space

TL;DR

This paper proposes a simple model for stabilizing extra dimensions in string theory using brane winding and momentum modes, showing that stabilization occurs for three or fewer observed spatial dimensions depending on the gravity theory.

Contribution

It introduces a symmetric decimation model with all extra dimensions as tori, demonstrating stabilization conditions independent of the decimation parameter p.

Findings

Extra dimensions can be stabilized with brane winding modes.

Stabilization conditions depend on the number of observed space dimensions.

Solutions exist for both Einstein and dilaton gravity cases.

Abstract

We present a simple model for the late time stabilization of extra dimensions. The basic idea is that brane solutions wrapped around extra dimensions, which is allowed by string theory, will resist expansion due to their winding mode. The momentum modes in principle work in the opposite way. It is this interplay that leads to dynamical stabilization. We use the idea of democratic wrapping \cite{art5}-\cite{art6}, where in a given decimation of extra dimensions, all possible winding cases are considered. To simplify the study further we assumed a symmetric decimation in which the total number of extra dimensions is taken to be $Np$ where N can be called the order of the decimation. We also assumed that extra dimensions all have the topology of tori. We show that with these rather conservative assumptions, there exists solutions to the field equations in which the extra dimensions are stabilized and that the conditions do not depend on $p$. This fact means that there exists at least one solution to the asymmetric decimation case. If we denote the number of observed space dimensions (excluding time) by $m$, the condition for stabilization is $m\geq 3$ for pure Einstein gravity and $m\leq 3$ for dilaton gravity massaged by string theory parameters.