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Register a new userOn the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
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The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplifie
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The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has been found recently, however, that the matrix configurations generated by the simulation is singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem has been attributed to the approximation used to avoid the sign problem in simulating the model. Here we investigate the model using the complex Langevin method to overcome the sign problem instead of using the approximation. Our results indicate a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior is kept intact.
We review recent developments in the type IIB matrix model, which was conjectured to be a nonperturbative formulation of superstring theory. In the first part we review the recent results for the Euclidean model, which suggest that SO(10) symmetry is spontaneously broken. In the second part we review the recent results for the Lorentzian model. In particular, we discuss Monte Carlo results, which suggest that (3+1)-dimensional expanding universe emerges dynamically. We also discuss some results suggesting the emergence of exponential expansion and the power-law expansion at later times. The behaviors at much later times are studied by the classical equation of motion. We discuss a solution representing 3d expanding space, which suggests a possible solution to the cosmological constant problem.
The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In the Lorentzian version, in particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. Here we provide new perspectives on the (3+1)D expanding space-time that have arised from recent studies. First it was found that the matrix configurations generated by the simulation are singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem was conjectured to occur due to the approximation used to avoid the sign problem in simulating the model. In order to confirm this conjecture, the complex Langevin method was applied to overcome the sign problem instead of using the approximation. The results indeed showed a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior remained unaltered. It was also found that classical solutions obtained within a certain ansatz show quite generically a (3+1)D expanding behavior with smooth space-time structure.
We study the Lorentzian version of the type IIB matrix model as a nonperturbative formulation of superstring theory in (9+1)-dimensions. Monte Carlo results show that not only space but also time emerges dynamically in this model. Furthermore, the real-time dynamics extracted from the matrices turns out to be remarkable: 3 out of 9 spatial directions start to expand at some critical time. This can be interpreted as the birth of our Universe.
Assuming that the large-$N$ master field of the Lorentzian IIB matrix model has been obtained, we go through the procedure of how the coordinates of emerging spacetime points can be extracted. Explicit calculations with test master fields suggest that the genuine IIB-matrix-model master field may have a fine-structure that is essential for producing the spacetime points of an expanding universe.
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