Quantum Gravity・String Theory

Gravity is probably the first fundamental force that people recognized in history. Nevertheless, a complete theoretical framework of gravity has not been found yet. Currently, the most reliable theory of gravity is Einstein's general relativity. However, it is known that, when we naively apply the principle of quantum theory to gravity, various theoretical calculations of physical quantities turn out to be divergent. A consistent theory of quantum gravity is indispensable to understand the physics with extremely strong gravity such as the cases with singularities at the beginning of the universe or inside the black hole, etc. Solving these problems and constructing a consistent theory of quantum gravity is one of the most important problems in theoretical physics.

At present, many researchers believe that string theory is the leading candidate for quantum gravity. It is a theory based on the hypothesis that all the elementary particles in nature are made of tiny strings rather than point particles. String theory naturally contains gravity and even if the quantum corrections are included, the infinities in perturbative calculations of quantum gravity are miraculously canceled. In addition, it was shown in the 1980s that it could reproduce the grand unified theory that unifies all the other fundamental forces (electromagnetic force, weak force, strong force). For these reasons, people considered it to be a candidate for the ultimate unified theory.

The research subject of string theory has expanded dramatically since the revolutionary development called the ``second superstring revolution'' started from the mid 1990s. In particular, various intimate relations between string theory and quantum field theory have been found. String theory has been applied to solve problems in quantum field theory and the knowledge of quantum field theory has been used in the analysis of string theory. (The "gauge/gravity correspondence" described below was also discovered from such research activities.) This trend is continuing and we are developing the ideas in various directions, for example, application of string theory to find dualities in quantum field theory, elucidation of the mathematical structure of supersymmetric theories, understanding of mechanisms of confinement in strongly coupled gauge theory, studying properties of black holes, etc.

If string theory is a correct theory of quantum gravity, it should shed some light on quantum properties of black holes. It is conjectured that black holes emit lights, matters, etc., and eventually evaporate. However, as Hawking pointed out in the 1970s, this process seems to contradict with the unitarity, which is one of the fundamental principles in quantum theory, because the information went inside of the black hole seems to be lost. A clear resolution of this paradox is still lacking. There are some situations that microscopic degrees of freedom of a black hole, that explain the microscopic origin of the black hole entropy, can be identified by embedding black holes in string theory. There are some attempts to solve the black hole information loss paradox by investigating such microscopic descriptions of black holes.

Currently, the formulation of string theory is given in terms of perturbation theory. Although there are a lot of non-perturbative properties known in string theory that people have uncovered by using, e.g., dualities or correspondences to quantum field theory, a precise non-perturbative formulation of string theory is not yet available. There are many approaches to this problem, including matrix models, string field theory, etc., which have been actively studied. More recently, a formulation of string theory via quantum field theory based on gauge/gravity correspondence, is also discussed as a promising approach. See the next entry ``gauge/gravity correspondence'' for more details on this subject.

Of course, string theory is not yet established as the ultimate theory describing our world. There are other attempts to construct consistent formulations of quantum gravity. Besides, phenomenological studies of elementary particles, such as models with supergravity and/or extra dimensions, are also expected to give some important implications to the physics of gravity. Our research is not limited to those mentioned above. We try to explore new theories beyond the boundaries of existing theories with unfettered imagination.

Gauge/Gravity Correspondence

The gauge/gravity correspondence is a remarkable phenomenon, first discovered by Juan Maldacena in 1997, where gravitational theories are equivalent to non-gravitational theories which describe various matter systems. In theoretical physics, general relativity which predicts evolutions of universe and quantum theories for particles and condensed matter systems have been studied separately. However, if we assume the gauge/gravity correspondence, then these two different classes of theories become equivalent. In this way, the gauge/gravity correspondence is expected to be developed into a new framework which may change basic ideas of theoretical physics.

To develop a microscopic theory of gravity (quantum gravity) is very important to understand how our universe was created and is one of the most difficult problems in theoretical physics. However, if we apply the gauge/gravity correspondence, we can change this difficult problem into a much tractable problem in a quantum system. Therefore the gauge/gravity correspondence is expected to be a powerful method to resolve problems in quantum gravity and developing this approach is one of the main aims of this research division.

For this purpose we need to understand the basic principle of gauge/gravity correspondence. It has been already passed 20 years since the gauge/gravity correspondence was discovered and there have been numerous papers published which verify this correspondence in various examples. However, we are still not able to explain why the gauge/gravity correspondence occurs and in this sense, the gauge/gravity correspondence is a sort of a black box even now. Nevertheless, a new tool has recently been available to attack this long standing problem. This is the phenomenon called quantum entanglement and it describes a correlation which appear only in quantum theories not in classical ones. The quantum entanglement can be interpreted as the potential of acting quantum operations in quantum information theory and also has been used as a quantum order parameter which describes the degrees of freedom in quantum systems. By analyzing the gauge/gravity correspondence from the viewpoint of quantum entanglement, a novel expectation has been obtained which tells us that the structures of quantum entanglement in quantum systems correspond to the geometry of universe in gravity. In order to realize this idea explicitly, we need to combine the methods in gravity, quantum field theories and quantum information theories.

Another aim of this research division is to apply the gauge/gravity correspondence to studies of various condensed matter systems. In the gauge/gravity correspondence, if we consider the general relativity as a theory of gravity, ignoring quantum gravity effects, it corresponds to a very strongly interacting quantum system such as QCD. Though in general, it is very difficult to directly analyze strongly interacting systems, we can employ the gauge/gravity correspondence to replace this quantum problem with a much simpler one of classical gravity in a black hole spacetime. In this way, we can apply the gauge/gravity correspondence to studies of various quantum systems such as nuclear physics, QCD, condensed matter systems and non-equilibrium physics. To develop further these applications is a very important subject which can widely contribute to progresses of theoretical physics. In summary, the purpose of this research division is to explore the basic principle of gauge/gravity correspondence and its applications aiming at a unification of various subjects in theoretical physics.

Grvitational Wave Astronomy

In September, 2015, US gravitational wave detectors, advanced LIGO, achieved the first direct detection of gravitational waves emitted from binary black holes. Japanese gravitational-wave community has been developing another gravitational wave detector, named KAGRA, and it will start the observational run from 2018. If these detectors start observation with their design sensitivity, gravitational waves from binary black holes and binary neutron stars will be detected almost every day. Then, we will be able to learn in depth the strong self-gravitating phenomena, which are still poorly known. In addition, gravitational-wave observation will give a strong impact on the high-energy astrophysics. For example, if a core collapse supernova explosion or a gamma-ray burst occurs in the nearby galaxies, gravitational waves will be observed and we will get rich information for these phenomena, which are also poorly understood. Furthermore, the gravitational-wave observation will be used for testing general relativity. If we are lucky, we may be able to get evidence for the violation of general relativistic prediction in detected gravitational waves.

In the gravitational-wave astronomy, the role of theoretical researchers is quite important. The reason for this is that for the detection of gravitational waves from noisy data and for the determination of the parameters of gravitational-wave sources, we need a highly accurate gravitational wave templates by analyzing Einstein's equation. Developing efficient data-analysis methods is also the urgent issues in this field.

It is also quite important to predict electromagnetic signals that could be emitted together with the gravitational-wave signals. Coincident detection of electromagnetic signals with gravitational waves will enhance the reliability of the gravitational-wave detection. Furthermore, electromagnetic signals will bring rich information which cannot be obtained only from gravitational wave signals. To establish the gravitational-wave astronomy, we have to also develop an efficient method for the detection of electromagnetic signals. For this task, theoretical prediction of electromagnetic signals is quite important.

As all of these statements show, the gravitational-wave astronomy has just begun and now is the exciting era. There are many topics to which theoretical physicist can contribute. One of the important roles of Center for Gravitational Physics is to enhance the Japanese activity in the gravitational-wave astronomy as the theoretical physics center in Japan. The other important role is to encourage the international collaboration among a wide variety of researchers in the gravitational-wave astronomy.

Cosmology and extended theories of gravity

Cosmology has been rapidly developing, based on precision observational data. It is fair to say that many parameters describing our universe have been determined, or at least are in the process of being determined, with good precision. However, the physics behind the values of these parameters is still hidden in a veil of mystery. For example, we do not know what dark energy and dark matter really are, although our universe is thought to be filled mostly with them. Also, what made our universe so big? This question can be addressed by cosmic inflation, but again we do not know the physical origin of the inflaton field driving inflation. Three great mysteries, dark energy, dark matter and inflation, are standing in the way of cosmology which boasts precision observational data. We need to continue tackling the mysteries of the universe by using every possible means such as general relativity, statistical physics, particle physics and superstring theory.

In our universe physical phenomena at various scales occur constantly, having mutual influence on each other. We consider it necessary for physics at the largest scales, i.e. cosmology, to be connected with physics at the shortest scales. This is because the extremely high energy state of the early universe makes microscopic physics essentially important. At the beginning of the universe, both gravity and quantum effects are significant and, as a result, both general relativity and the conventionsl quantum field theory break down. For this and many other reasons, we need a theory of quantum gravity that can describe gravity in a quantum mechanically consistent way. Cosmology based on quantum gravity should play important roles in our understanding of the universe.

The cosmological constant (cc) problem is one of the most difficult problems in theoretical physics and cosmology. There are two aspects of the cc problem. The first is "Why small?" The observational upper bound on the cc is smaller than what is naively expected quantum mechanically by 120 orders of magnitude. At present there is no theory that can convincingly explain this small value. For this reason, some researchers show a tendency to rely on the anthropic principle. However, I consider it premature to give up seeking a solution without the anthropic principle. If a new theory that solves the cc problem based on physical principles is found then the anthropic "solution" will soon be forgotten. We should not give up attempting difficult problems.

The second aspect of the cc problem is "Why not zero?" and "Why now?" This is nothing but one of the three great mysteries of the universe, dark energy. Although dark energy is thought to fill more than 70% of the present universe, we do not know what it really is. This situation makes us feel that a hint for new physics may be hidden in gravity at cosmological scales. Evidences for dark energy so far are based on indirect observations of gravity at long distance and time scales but gravity at such scales has never been measured directly. When the perihelion shift of Mercury was discovered in the Nineteen Century, some people tried to explain this interesting phenomenon by introducing an unknown planet, so to speak dark planet. Some people even "discovered" it. As we all know, however, the right answer was not a dark planet but to change gravity, from Newton's theory to Einstein's general relativity. This was indeed the beginning of the success of the new theory. With this historical fact in mind, it it understandable that many researchers now think that the mystery of the accelerated expansion of the universe might be similar. People thus recently started to ask "Can we change general relativity at long distance or/and time scales instead of introducing dark energy or/and dark matter?" Needless to say, however, it is observations and experiments that give a decision. To answer the question "dark energy or modification of gravity?", we need to construct a theoretically consistent and observationally viable theory of gravity and derive verifiable predictions.

Quantum Information Theory

Quantum theory is known to exhibit many "strange" phenomena, such as entanglement, coherence, etc. One of the most central research goals of quantum information is to control these strange phenomena to realize new information processing tasks, such as secure crypto-communication and super-fast computing. In fact, it is known that unconditionally secure key distribution is possible with entanglement (quantum key distribution), and some problems that are not known to be solved efficiently with classical computing can be solved with quantum computing in polynomial time. These theoretical ideas have recently been implemented by not only experimentalists in academia but also engineers in companies such as Google, IBM, and Microsoft. Our group has proposed several theoretical protocols that enable secure cloud quantum computing (blind quantum computing), and showed quantum supremacy of some sub-universal quantum computing models.

Another important goal of quantum information is to feedback results obtained in quantum information to physics. In fact, many new concepts, ideas, techniques have been imported to the traditional physics, such as statistical physics, condensed matter physics, particle physics, and gravity, etc. Our group has also contributed in this direction. For example, we have shown several new results between physical properties of quantum many-body states (such as entanglement, correlations, and topological order, etc.) and power of quantum computing through the tensor-network representation of measurement based quantum computing. We have also shown several relations between partition functions of classical Ising models and quantum computing. Quantum computational complexity theory is one of the central research subjects in computer science. Recently, it has been attracting much attentions among physicists, since several important physical quantities in physics are clearly characterized by using quantum computational complexity theory. Our group has studied relations between quantum interactive proof systems and physics.

In this way, we aim at the mutual fertilization between physics and information science through quantum information.