Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Space-Time Structures from IIB Matrix Model

H. Aoki, S. Iso, H. Kawai, Y. Kitazawa, T. Tada

Abstract

We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite $N$ to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.

Space-Time Structures from IIB Matrix Model

Abstract

We derive a long distance effective action for space-time coordinates from a IIB matrix model. It provides us an effective tool to study the structures of space-time. We prove the finiteness of the theory for finite to all orders of the perturbation theory. Space-time is shown to be inseparable and its dimensionality is dynamically determined. The IIB matrix model contains a mechanism to ensure the vanishing cosmological constant which does not rely on the manifest supersymmetry. We discuss possible mechanisms to obtain realistic dimensionality and gauge groups from the IIB matrix model.

Paper Structure

This paper contains 17 sections, 107 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Effective theory for diagonal elements
  3. Perturbative evaluation of $S_{\rm eff}[X,\xi]$
  4. ${\cal N}=2$ SUSY
  5. Dynamics of X at long distances
  6. One loop evaluation of $S_{\rm eff}[X]$
  7. Infrared convergence
  8. Short distances
  9. Possible scenarios of dynamical generation of space-time
  10. Models
  11. Branched polymer phase and droplet phase
  12. A mechanism favoring lower dimensions
  13. Other mechanisms for understanding space-time structure
  14. Conclusions and Discussions
  15. Fierz transformation
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Numerical simulation for $N=1000$ . Horizontal axis is $\lambda$. Stars indicate root mean squares of the eigenvalues and dots indicate the ratio of 16-fold bonds. For large values of $\lambda$, the system is in a BP phase. For small values of $\lambda$, it is in a droplet phase.
  • Figure 2: Free energy as a function of dimensions. We take $\gamma=17/6$. Free energy is minimized at four dimensions.
  • Figure 3: Graphical representation of a two point function. A pair of points in a given configuration can be connected by bonds in a unique way. In this figure they are connected by five bonds. Such bonds form a random walk type object. The remaining points in a branched polymer are connected to the points in this object. They are represented by the blobs in this figure.
  • Figure 4: Graphical representation of the Schwinger Dyson equation for $b$. White circles is not associated with any wight.
  • Figure 5: Typical relation between $k$ and $b$ is drawn. A black dot in the figure indicates the critical point. The large $N$ limit is taken by approaching this point from the left.