The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913053545594880 |
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| author | Anagnostopoulos, Konstantinos N. Azuma, Takehiro Hirasawa, Mitsuaki Nishimura, Jun Papadoudis, Stratos Tsuchiya, Asato |
| author_facet | Anagnostopoulos, Konstantinos N. Azuma, Takehiro Hirasawa, Mitsuaki Nishimura, Jun Papadoudis, Stratos Tsuchiya, Asato |
| contents | The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, the eigenvalue distribution of the $N\times N$ bosonic matrices $A_μ$ $(μ= 0 , \ldots , 9)$ represents an emergent spacetime, which is determined by the dynamics of the model in the large-$N$ limit. Here we perform numerical simulations of the model overcoming the sign problem by the complex Langevin method with the matrix size $N$ up to $128$. In order to avoid the singular drift problem due to the Pfaffian, which appears after integrating out the fermionic matrices, we deform the model in a manner inspired by the supersymmetric deformation, which is used to define the ``polarized type IIB matrix model'' in the Euclidean case. We find that the deformed model exhibits a phase in which (3+1)-dimensional expanding spacetime emerges with both space and time being smooth and real. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations Anagnostopoulos, Konstantinos N. Azuma, Takehiro Hirasawa, Mitsuaki Nishimura, Jun Papadoudis, Stratos Tsuchiya, Asato High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Lattice The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, the eigenvalue distribution of the $N\times N$ bosonic matrices $A_μ$ $(μ= 0 , \ldots , 9)$ represents an emergent spacetime, which is determined by the dynamics of the model in the large-$N$ limit. Here we perform numerical simulations of the model overcoming the sign problem by the complex Langevin method with the matrix size $N$ up to $128$. In order to avoid the singular drift problem due to the Pfaffian, which appears after integrating out the fermionic matrices, we deform the model in a manner inspired by the supersymmetric deformation, which is used to define the ``polarized type IIB matrix model'' in the Euclidean case. We find that the deformed model exhibits a phase in which (3+1)-dimensional expanding spacetime emerges with both space and time being smooth and real. |
| title | The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2604.19836 |