Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model

Abstract

The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing "infrared" cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power ($2p$) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of $p$ and hence universal for $p\gtrsim 1.3$. For $p$ as large as 2.0, however, we find that large-$N$ scaling behaviors do not show up, and we cannot take a sensible large-$N$ limit. Thus we find that there is a certain range of $p$ in which a universal large-$N$ limit can be taken. Within this range of $p$, the dynamical space-time dimensionality turns out to be $(3+1)$, while for $p=2.0$, where we cannot take a sensible large-$N$ limit, we observe a (5+1)d structure.

20 pages, 26 figures

References in corpus (5)

• Cosmological solutions of emergent noncommutative gravity
• Emergent Spacetime and The Origin of Gravity
• Emergent gravity on covariant quantum spaces in the IKKT model
• Matrix Model Approach to Cosmology
• Dynamical phase space from a SO(d,d) matrix model

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• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
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• Dimensional deformation of sine-Gordon breathers into oscillons