Difficulty in the quantization of gravity

At present, physical phenomena obserbed by accelerator experiments are well described by the standard model. In this model matter consists of fundamental particles, quarks and leptons, and we can treat quantum mechanically three fundamental interactions (electromagnetic interaction, weak interaction and strong interation) between these particles.

Gravity is well-known as another fundamental interaction. Gravity is classically represented as curvature of space-time and described by Einstein's general relativity. However, it has been known that there is a great difficulty in dealing with gravity quantum mechanically unlike the other three forces. This means that the two basis of theoretical physics, namely, general relativity and quantum theory, is not consistently combined with each other. Quantization of gravity is one of the most important problem in particle physics.

Necessity of the fundamental theory that describes the Planck scale physics

Fortunately or not, gravity between particles is extremely weak in the phenomena obserbed in usual accelerator experiments, so that there is no problem in ignoring it. However, it is anticipated that we cannot ignore gravity if particles are accelerateed to about the Planck scale�i10^19 GeV (‚P‚X‚Í�ã•t‚«‚Å‚·)�jand collide with each other. In addition, quantum gravity is indispensable to understand the black hole evaporation and the early universe.

These difficulties in the quantization of gravity mean that we still do not know the theory that describes physics at extremely high energy scale or extremely small scale. Moreover, the standard model includes no less than seventeen parameters which we must determine from experimental results. Therefore, it is natural to think that these parameters are determined from more microscopic theory hidden behind it, as the history of science tells us. The standard model without gravity has many unnatural factors, such as the hierarchy problem. There is a possibility that answers to them are derived from fundamental theory which describes physics at the smaller scale than the Planck length.

Superstring theory as the `theory of every thing'

One of the natural approach to quantum gravity is superstring theory. In this theory we treat particles as one-dimensional extended objects, namely, strings instead of points. Since strings have several oscillation modes unlike points, single string can represent various kind of particles. Astonishingly, the particles realized in such a way automatically includes graviton which mediate gravity. Moreover, since we deal with extended strings as fundamental elements, we can avoid the difficulty which arise when we quantize gravity in the usual framework of point particle theory.

We are fascinated with superstring theory not only because it describes the quantization of gravity correctly but also because there is a possibility that it explains in principle not only parameters in the standard model but also gauge group, generation number and dimensions of space-time, although it has no dimensionless parameter. For this reason, superstring theory has been often called `theory of everything', and investigated energetically from 1980's. Although at present God only knows how far is it from here to the goal, several ideas are suggested recent years as we will mention below, and things are begining to take on the aspects of the dawn of superstrings.

D-brane, duality, M-theory

The most important problem in superstring theory is the existence of infinite number of stable perturbative vacuums. Thus, non-perturbative approarch is essential to understand the properties of the true vacuum which is expected to describe our world. Investigation in this direction has proceeded from the middle of 1990's, and non-perturbative effects of strings has been understood step by step. This progress is stimurated by the discovery of a soliton solution called `D-brane' in string theory and the identification of several string theories (it is called `duality') by making use of it. The perspective on string theory has changed through these discoveries, and it is believed that there exist more fundamental theory than string theory and string theory appears as an aspect of this theory. This unknown fundamental theory is called `M-theory'. `M' is said to be the abbreviation of mystery, mother, matrix etc.

Non-perturbative analysis of superstrings via matrix model

In this sequence of discovery, non-perturbative formulation of superstrings via matrix model was proposed in 1996. This matrix model corresponds to lattice gauge theory in gauge theory. Therefore, it is expected that non-perturbative properties of superstrings become clear via matrix model, as it has become possible to understand quark confinement via lattice gauge theory. This matrix model was proposed by Kawai, Ishibashi and Tsuchiya, who belonged to the KEK theory group at that time, and Kitazawa, who is now the head of the KEK theory division. This model is called `IKKT model' after the initial letters of these people.

In the KEK theory group we have continuously investigated non-perturbative superstrings via matrix model since then. Many domestic and foreign researchers concentrate into the KEK theory group as posdocs or visitors. Recently, we have particularly investigated noncommutative geometry and dynamics of matrix model by using numerical simulation and analytical method vigorously. For example, space-time is treated as a dynamical object represented by an eigen value distribution of a matrix in the IKKT model, and it becomes clear by investigating such a quantity that the 4-dimensional space-time in which we live is generated dynamically in type IIB superstring thoery formulated in 10-dimensional space-time.

Another aspect of matrix model

More recently, it become clear from another point of view that matrix model is closely related to superstring theory. `Random simplicial decomposition' is one of the approach to quantum gravity as is mentioned in `4. Gravity, fundamental aspects of quantum theory'. `Random matrix model', which realize this `random simplicial decomposition', is related to superstring theory, topological string theory and supersymmetric gauge theory. Although this model itself has no supersymmetry, we can see that it has so-called `integrable structure' since it follows infinite number of differential equations. We can also find out that we can calculate physical quantities concerning superstring theory or its effective gauge theory on the 4-dimensional space-time obtained from 10-dimensional space-time compactified on the Calabi-Yau space (6-dimension) by using this model. In the KEK theory group we carry on the investigation of matrix model from various points of view like this.