On the Origin of the $SO(9) \rightarrow SO(3) \times SO(6)$ Symmetry Breaking in the IKKT Matrix Model

TL;DR

This paper proposes a dynamical mechanism within the IKKT matrix model explaining why the symmetry breaks from SO(9) to SO(3)×SO(6), leading to three large spatial dimensions through D1-string interactions.

Contribution

It introduces a novel explanation for symmetry breaking in the IKKT model based on D1-string dynamics and their intersection properties.

Findings

Symmetry breaks from SO(9) to SO(3)×SO(6) in the model.

Large spatial dimensions emerge when D1-strings can annihilate.

The mechanism relies on the suppression of string intersections in higher dimensions.

Abstract

We suggest a dynamical mechanism which explains why in the supersymmetric IKKT matrix model the $SO(9)$ symmetry of the Lagrangian is spontaneously broken to $SO(3) \times SO(6)$, allowing only three large classical spatial dimensions to emerge. The argument relies on the identification of D1-strings as stable excitations of the matrices about the cosmological background, and the absence of forces between parallel D1-string excitations. A spatial dimension can only become large if the D1-strings winding that direction can annihilate. In the absence of forces, this requires the string world sheets to intersect, a process which is highly suppressed if more than three dimensions of space are large. Implications for a recently proposed matrix cosmology scenario are discussed.