Systematic study of the SO(10) symmetry breaking vacua in the matrix model for type IIB superstrings

TL;DR

This paper investigates the emergent space-time structure from the type IIB matrix model, analyzing various symmetry-breaking vacua and revealing systematic properties and a preference for three-dimensional space-time.

Contribution

It provides a systematic study of SO(d) symmetric vacua for 2 ≤ d ≤ 7 in the matrix model, highlighting properties of the emergent space-time and identifying d=3 as energetically favored.

Findings

The extent in shrunken directions is constant across d.

The ten-dimensional volume is constant except at d=2.

Free energy is minimized at d=3.

Abstract

We study the properties of the space-time that emerges dynamically from the matrix model for type IIB superstrings in ten dimensions. We calculate the free energy and the extent of space-time using the Gaussian expansion method up to the third order. Unlike previous works, we study the SO(d) symmetric vacua with all possible values of d within the range $2 \le d \le 7$, and observe clear indication of plateaus in the parameter space of the Gaussian action, which is crucial for the results to be reliable. The obtained results indeed exhibit systematic dependence on d, which turns out to be surprisingly similar to what was observed recently in an analogous work on the six-dimensional version of the model. In particular, we find the following properties: i) the extent in the shrunken directions is given by a constant, which does not depend on d; ii) the ten-dimensional volume of the Euclidean space-time is given by a constant, which does not depend on d except for d = 2; iii) The free energy takes the minimum value at d = 3. Intuitive understanding of these results is given by using the low-energy effective theory and some Monte Carlo results.