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Recently we have shown by Monte Carlo simulation that expanding (3+1)-dimensional universe appears dynamically from a Lorentzian matrix model for type IIB superstring theory in (9+1)-dimensions.
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The mechanism of the spontaneous breaking in the Euclidean model [ 10 , 11 ] is quite different from that in the Lorentzian model. In the former, the Pfaffian that appears from the fermion integral is complex, and it becomes real positive for collapsed configurations
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This quantity may be related to the space-time uncertainty principle. See e.g., Ref. [ 17 ]
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