Complex Langevin studies of the emergent space–time in the type IIB matrix model

Hatakeyama, Kohta; Αναγνωστόπουλος, Κωνσταντίνος; Azuma, Takehiro; Hirasawa, Mitsuaki; Ito, Yuta; Nishimura, Jun; Papadoudis, Stratos; Tsuchiya, Asato

doi:10.1142/9789811261633_0002

“…This contour deformation amounts to multiplying some phase factors to the temporal and spatial matrices, which is allowed since there is no singularity that one has to go through. We can confirm explicitly that the Lorentzian version is indeed equivalent to the Euclidean version by measuring correlation functions, which are identical up to some phase factors [3,4]. Since the emergent space-time in the Euclidean version has Euclidean signature, the equivalence between the Lorentzian and Euclidean versions clearly poses a big challenge in obtaining a Lorentzian space-time in the IKKT model.…”

Section: Introductionmentioning

confidence: 52%

“…Let us emphasize that the sign of the mass term ( 11) is crucial. For 𝛾 < 0, we have Im𝑆 m > 0 for 0 < 𝑠 < 4 3 , which enables us to connect the theory to the Euclidean model with the mass term (14), which is well defined. Therefore the situation is qualitatively the same as in the 𝛾 = 0 case, and nothing dramatic happens.…”

Section: Adding a Lorentz Invariant "Mass" Termmentioning

confidence: 99%

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Signature change of the emergent space-time in the IKKT matrix model

Nishimura¹

2022

Preprint

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The IKKT matrix model (or the type IIB matrix model) is known as a promising candidate for a nonperturbative formulation of superstring theory in ten dimensions. As a most attractive feature, the model admits the emergence of (3+1)-dimensional space-time associated with the spontaneous breaking of the (9+1)-dimensional Lorentz symmetry. Numerical confirmation of such a phenomenon has been attempted for more than two decades. Recently it has been found that the sign problem, the main obstacle in simulating this model, can be overcome by the complex Langevin method. It has been shown that the Lorenzian version of the model is smoothly connected with the Euclidean version, in which the SO(10) symmetry is found to be spontaneously broken to SO(3). Here we propose to add a Lorentz invariant "mass" term to the original model and discuss a scenario that (3+1)-dimensional expanding space-time with Lorentzian signature appears at late times. Some numerical results supporting this scenario are presented.

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“…Let us emphasize that the sign of the mass term ( 11) is crucial. For < 0, we have Im m > 0 for 0 < < 4 3 , which enables us to connect the theory to the Euclidean model with the mass term (14), which is well defined. Therefore the situation is qualitatively the same as in the = 0 case, and nothing dramatic happens.…”

Section: Jun Nishimuramentioning

confidence: 99%

Signature change of the emergent space-time in the IKKT matrix model

Nishimura¹

2022

Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)

8

0

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The IKKT matrix model (or the type IIB matrix model) is known as a promising candidate for a nonperturbative formulation of superstring theory in ten dimensions. As a most attractive feature, the model admits the emergence of (3+1)-dimensional space-time associated with the spontaneous breaking of the (9+1)-dimensional Lorentz symmetry. Numerical confirmation of such a phenomenon has been attempted for more than two decades. Recently it has been found that the sign problem, the main obstacle in simulating this model, can be overcome by the complex Langevin method. It has been shown that the Lorenzian version of the model is smoothly connected with the Euclidean version, in which the SO(10) symmetry is found to be spontaneously broken to SO(3). Here we propose to add a Lorentz invariant "mass" term to the original model and discuss a scenario that (3+1)-dimensional expanding space-time with Lorentzian signature appears at late times. Some numerical results supporting this scenario are presented.

show abstract

“…Over the past two decades there has been a lot of numerical work on this model (see e.g. [15][16][17] for reviews, and [18][19][20] for more recent numerical studies), and we will summarize the results which are relevant for our analysis. In section 3, we then show how continuous space-time with infinite extent of both space and time variables emerges, give a proposal for an emergent metric, and show that the resulting cosmological metric corresponds to a spatially flat manifold.…”

Section: Introductionmentioning

confidence: 99%

Emergent metric space-time from matrix theory

Brahma

¹

,

Brandenberger

²

,

Laliberte

³

2022

J. High Energ. Phys.

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The IKKT matrix model yields an emergent space-time. We further develop these ideas and give a proposal for an emergent metric. Based on previous numerical studies of this model, we provide evidence that the emergent space-time is continuous and infinite in extent, both in space and in time, and that the metric is spatially flat. The time evolution describes the transition from a string-theoretic emergent phase to a phase in which the SO(9) symmetry of the model is spontaneously broken to SO(6) × SO(3), with three dimensions of space expanding, becoming classical and at later times evolving like in a radiation-dominated universe, and the remaining six dimensions of space stabilized at the string scale. We speculate on how this analysis can be extended to yield an early universe cosmology which, in addition to the above-mentioned properties, also leads to a roughly scale-invariant spectrum of cosmological fluctuations and gravitational waves.

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Complex Langevin studies of the emergent space–time in the type IIB matrix model

Cited by 8 publications

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Signature change of the emergent space-time in the IKKT matrix model

Signature change of the emergent space-time in the IKKT matrix model

Signature change of the emergent space-time in the IKKT matrix model

Emergent metric space-time from matrix theory

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