High Energy Accelerator Research Organization (KEK)

Public Relation Office, Head

Hajime Hikino

E-mail：press@mail.kek.jp

# a 40-year-old puzzle of superstring theory solved by supercomputer

## The mechanism that explains why our universe was born with 3 dimensions:

A group of three researchers from KEK, Shizuoka University and Osaka University has for the first time revealed the way our universe was born with 3 spatial dimensions from 10-dimensional superstring theory^{1} in which spacetime has 9 spatial directions and 1 temporal direction. This result was obtained by numerical simulation on a supercomputer.

**[Abstract]**

According to Big Bang cosmology, the universe originated in an explosion from an invisibly tiny point. This theory is strongly supported by observation of the cosmic microwave background^{2} and the relative abundance of elements. However, a situation in which the whole universe is a tiny point exceeds the reach of Einstein's general theory of relativity, and for that reason it has not been possible to clarify how the universe actually originated.

In superstring theory, which is considered to be the "theory of everything", all the elementary particles are represented as various oscillation modes of very tiny strings. Among those oscillation modes, there is one that corresponds to a particle that mediates gravity, and thus the general theory of relativity can be naturally extended to the scale of elementary particles. Therefore, it is expected that superstring theory allows the investigation of the birth of the universe. However, actual calculation has been intractable because the interaction between strings is strong, so all investigation thus far has been restricted to discussing various models or scenarios.

Superstring theory predicts a space with 9 dimensions^{3}, which poses the big puzzle of how this can be consistent with the 3-dimensional space that we live in.

A group of 3 researchers, Jun Nishimura (associate professor at KEK), Asato Tsuchiya (associate professor at Shizuoka University) and Sang-Woo Kim (project researcher at Osaka University) has succeeded in simulating the birth of the universe, using a supercomputer for calculations based on superstring theory. This showed that the universe had 9 spatial dimensions at the beginning, but only 3 of these underwent expansion at some point in time.

This work will be published soon in Physical Review Letters.

**[The content of the research]**

In this study, the team established a method for calculating large matrices (in the IKKT matrix model^{4}), which represent the interactions of strings, and calculated how the 9-dimensional space changes with time. In the figure, the spatial extents in 9 directions are plotted against time.

If one goes far enough back in time, space is indeed extended in 9 directions, but then at some point only 3 of those directions start to expand rapidly. This result demonstrates, for the first time, that the 3-dimensional space that we are living in indeed emerges from the 9-dimensional space that superstring theory predicts.

This calculation was carried out on the supercomputer Hitachi SR16000 (theoretical performance: 90.3 TFLOPS) at the Yukawa Institute for Theoretical Physics of Kyoto University.

**[The significance of the research]**

It is almost 40 years since superstring theory was proposed as the theory of everything, extending the general theory of relativity to the scale of elementary particles. However, its validity and its usefulness remained unclear due to the difficulty of performing actual calculations. The newly obtained solution to the space-time dimensionality puzzle strongly supports the validity of the theory.

Furthermore, the establishment of a new method to analyze superstring theory using computers opens up the possibility of applying this theory to various problems. For instance, it should now be possible to provide a theoretical understanding of the inflation^{5} that is believed to have taken place in the early universe, and also the accelerating expansion of the universe^{6}, whose discovery earned the Nobel Prize in Physics this year. It is expected that superstring theory will develop further and play an important role in solving such puzzles in particle physics as the existence of the dark matter that is suggested by cosmological observations, and the Higgs particle, which is expected to be discovered by LHC experiments^{7}.

### Glossary

**[1] Superstring theory**

There are four fundamental interactions among elementary particles: electromagnetic force, weak interaction, strong interaction and gravity. There is a theory that describes three interactions but not gravity, and a particle theory including gravity is still under investigation from various directions.

In superstring theory, all the elementary particles are represented as various oscillation modes of strings of tiny length, and thus the four interactions including gravity are described in a unified manner.

**[2] Cosmic microwave background**

Microwaves that come uniformly from the universe in all directions. They are considered to be the glow of the embers of the Big Bang, providing strong evidence for Big Bang cosmology, which claims that the universe is expanding after a big explosion.

The cosmic microwave background was discovered accidentally by Penzias and Wilson of the United States, who received the Nobel Prize in Physics in 1978. In recent years, more precise observation is being performed by the WMAP (Wilkinson Microwave Anisotropy Probe) launched by NASA (the National Aeronautics and Space Administration), and its observations have led to many important new understandings in cosmology.

**[3] 9 dimensions**

While the space we are living in has 3 dimensions, it is known in superstring theory that the space has to have 9 dimensions for consistency with quantum mechanics. Therefore, 6 of the 9 dimensions must somehow be invisible.

A popular approach is called "compactification", in which the extra 6 spatial dimensions curl up very small, but this presents a problem because there are so many ways to actually do it.

**[4] IKKT matrix model**

A new formulation of superstring theory was proposed by Ishibashi, Kawai, Kitazawa and Tsuchiya in 1996. (IKKT represents the initials of the authors.) The conventional formulation of superstring theory is valid only when the interaction between strings is weak, so it is not suitable for application to real physical phenomena. The IKKT matrix model, which uses large matrices to represent the fundamental dynamical degrees of freedom, has been formulated in a way that is also valid when the interaction between strings is strong.

Earlier investigations were restricted to the analysis of the model that treats time as an imaginary variable for technical reasons, and the relationship to the real world was not clear from the results. In the present research, the technical difficulty of treating time as a real variable has been overcome, enabling for the first time the application of the model to cosmology by explicit calculations.

**[5] Inflation**

Inflation is a rapid accelerating expansion, which is considered to have taken place within a very short time interval after the birth of our universe. It was proposed by Katsuhiko Sato and Alan Guth independently in the early 1980s. Inflation not only provides natural solutions to various problems in Big Bang cosmology, but also succeeds in explaining some detailed properties of the cosmic microwave background.

However, the mechanism that drove the inflation has only been discussed with respect to various models, and the derivation of inflation from a fundamental theory like superstring theory still remains an important challenge.

**[6] Accelerating expansion of the universe**

According to Big Bang cosmology, the universe has been expanding since it originated about 13.7 billion years ago. It was thought that this cosmic expansion was decelerating until it was actually found to be accelerating in the present epoch based on observational data from the last decade or so. The Nobel Prize in Physics for 2011 was awarded for contributions that led to the discovery of the accelerating expansion based on observations of type Ia supernovae.

However, the observed accelerating expansion implies that a mysterious energy ("dark energy"), which is not diluted by expansion, should comprise more than 70 percent of the total energy of the universe, and this requires some clarification from the viewpoint of theoretical physics.

**[7] The Higgs particle, which is expected to be discovered by LHC experiments**

LHC is the abbreviation for the Large Hadron Collider, the largest accelerator in the world, which started operation in autumn 2008 at CERN (the European Organization for Nuclear Research), located in a suburb of Geneva.

"LHC experiments" refers to all the experiments that are carried out with the accelerator. One of the biggest aims of the LHC experiments is to discover the Higgs particle, which is the only undiscovered particle in the Standard Model of particle physics, and to get some hints for solving the related problems in theoretical particle physics. The Higgs particle has been introduced to provide the mechanism that gives mass to elementary particles, but it entails some peculiarities from the viewpoint of theoretical particle physics including gravity, which should be clarified from both experimental and theoretical sides.

### Media Contacts:

#### For research:

Jun Nishimura

High Energy Accelerator Research Organization, Japan

Tel: 81-29-864-5398, Fax: 81-29-864-5755

E-mail: jnishi@post.kek.jp

Asato Tsuchiya

Shizuoka University, Japan

Tel: 81-54-238-4737, Fax: 81-54-238-4737

E-mail: satsuch@ipc.shizuoka.ac.jp

Sang-Woo Kim

Osaka University, Japan

Tel: 81-6-6850-5729, Fax: 81-6-6850-5379

E-mail: sang@het.phys.sci.osaka-u.ac.jp

#### For public relations:

Youhei Morita

Public Relations Office,

High Energy Accelerator Research Organization, Japan

Tel: 81-29-879-6047, Fax: 81-29-879-6049

E-mail: press@kek.jp

Yoko Kitagawa

Public Relations Section, Public Relations Staff

Shizuoka University, Japan

Tel: 81-54-238-5179, Fax: 81-54-237-0089

E-mail: koho@adb.shizuoka.ac.jp

Masato Ikeda

Kazuhiko Nishinoue

Osaka University, Japan

Tel: 81-6-6850-5280, Fax: 81-6-6850-5288

E-mail: ri-syomu@office.osaka-u.ac.jp

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