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 $N$ 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.Comment: 39 pages, Latex, uses epsf and axodra

On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

“…The large N behavior of this quantity has been observed to amount to R new / √ g = 3.30(1) · N 1/4 , which is consistent with the prediction based on the low-energy effective theory [18].…”

“…In the IIB matrix model, the eigenvalues of the bosonic matrices A µ are interpreted as the space-time coordinates [2,18,23]. We adopt this point of view in the 4D model as well.…”

Non-commutative Yang–Mills in IIB matrix model

“…In fact we can in principle predict the dimensionality of spacetime, the gauge group and the matter contents by solving this model. We have already initiated such investigations in [3] [4]. We refer our recent review for more detailed expositions and references [5].…”

Spontaneous breakdown of Lorentz invariance in IIB matrix model

“…In Ref. [8], it has been shown that the effective potential for x iµ can be given by a branched-polymer like attractive interaction among N points in D-dimensional space-time represented by x iµ (i = 1, · · · , N). Now counting the power of x i in the partition function, the integration measure for x iµ gives…”