Abstract
Abstract The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. As such, it is expected to explain the origin of space–time and matter at the same time. This has been partially demonstrated by the previous Monte Carlo studies on the Lorentzian version of the model, which suggested the emergence of (3+1)-dimensional expanding space–time. Here we investigate the same model by solving numerically the classical equation of motion, which is expected to be valid at late times since the action becomes large due to the expansion of space. Many solutions are obtained by the gradient descent method starting from random matrix configurations, assuming a quasi-direct-product structure for the (3+1)-dimensions and the extra 6 dimensions. We find that these solutions generally admit the emergence of expanding space–time and a block-diagonal structure in the extra dimensions, the latter being important for the emergence of intersecting D-branes. For solutions corresponding to D-branes with appropriate dimensionality, the Dirac operator is shown to acquire a zero mode in the limit of infinite matrix size.
Highlights
Superstring theory has been investigated intensively as a unified theory including quantum gravity
R=1 In Fig. 5, we plot the eigenvalues of Q(t) for the same typical solution discussed above. We find that they are densely distributed at each time and that all the eigenvalues are growing with time in the t > 0 region. This is in sharp contrast to the results for the configurations obtained by the previous Monte Carlo studies of the Lorentzian type IIB matrix model [13], where only two of the eigenvalues grow with time, while the others remain small and constant
We have proposed a numerical method which enables us to solve the classical equation of motion of the type IIB matrix model
Summary
Superstring theory has been investigated intensively as a unified theory including quantum gravity. We focus on the type IIB matrix model [6], which is distinctive in that space and time emerges dynamically from the matrix degrees of freedom It was shown by Monte Carlo simulation that (3+1)-dimensional expanding space–time appears from the Lorentzian version of the model [8]. [14], where the sign problem was treated correctly by the complex Langevin method for a simpler bosonic Lorentzian model Based on this observation, it has been conjectured that a smooth (3+1)-dimensional expanding space–time should emerge dynamically from the Lorentzian type IIB matrix model in the large-N limit.
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