Why do we live in 3+1 dimensions?

TL;DR

The work addresses why we observe (3+1) dimensions by proposing a dynamical braneworld mechanism in Type IIB string theory: a 9+1 bulk filled with D$p$-branes leads to frequent intersections and reconnection, causing higher-dimensional branes ($p>3$) to evaporate into bulk gravitons and dilatons until only D3- (and possibly D1) branes remain, with one D3-brane acting as our Universe. A key result is the intersection condition $2p+1 \ge d-1$ in a $d$-dimensional bulk (here $d=10$), which implies $p\ge 4$ for generic intersections and evaporation pathways like $\text{D9} \to \text{D7} \to \text{D5}$. This scenario generates bulk entropy through brane evaporation and potential thermalization of bulk modes, offering a dynamical mechanism for dimensionality selection and a link to the Universe's entropy budget, while leaving gravity localization unaddressed. The proposal hinges on toroidal compactification, reconnection dynamics, tachyonic instabilities signaling brane reconnection, and a cascade that naturally favors a (3+1)-dimensional brane-world.

Abstract

In the context of string theory we argue that higher dimensional Dp-branes unwind and evaporate so that we are left with D3-branes embedded in a (9+1)-dimensional bulk. One of these D3-branes plays the role of our Universe. Within this picture, the evaporation of the higher dimensional Dp-branes provides the entropy of our Universe.

Figures (4)

• Figure 1: The projection of two D$p$-branes, denoted by 1 and 2, which intersect along a $p-1$ dimensional manifold along dimensions omitted in this figure. They intersect in the point $\Phi$. We choose periodic boundary conditions. In a toroidal geometry, point A is identified with B, and point C with D.
• Figure 2: The new D$p$-brane which results from the intersection of the two D-branes shown in Fig. 1. With respect to the directions shown in the figure, it no longer winds around the torus.
• Figure 3: Schematic representation of two intersecting branes and the open strings which are attached to both of them. They lead to an anti-aligment of the two branes.
• Figure 4: The interaction potential $V(\phi_1,\phi_2)$ for two D4-branes which intersect on a plane and have two directions which are not aligned. The diagonals $\phi_1=\phi_2$ and $\phi_1=\pi-\phi_2$ are symmetry axes of the potential. The potential is exactly zero for $\phi_1=\phi_2$ and negative everywhere else. A configuration initially in one of the four quadrants will always move to the closest boundary of the plot, which corresponds to an alignment or anti-alignment in one of the directions.