Quantization of gravity is the biggest problem in theoretical physics. The superstring theory is the most promising candidate of the complete theory that includes quantum gravity. Dr. Tadashi Takayanagi has made many brilliant achievements in the frontier of the string theory. In particular, the following three works are striking and distinguished contributions, which deserve the Yukawa-Kimura prize this year.
1. Matrix model for exactly solvable string theory in two dimensions It is quite challenging to analyze the usual string theory defined in 10-dimensions. However, the analysis becomes easier for type 0 string theory in two dimensions. For this case the analysis including non-perturbative effects is possible. In 2003, Dr. Takayanagi has, in collaboration with Dr. Toumbas, constructed a matrix model equivalent to this two-dimensional theory. This is so far a unique model which is non-perturbatively stable and exactly solvable on various background spacetimes involving complicated dynamics. By this work, it becomes possible to treat non-static spacetime such as the expanding universe. In addition, this model can be regarded as a matrix quantum mechanics on D0-brane (D-brane in zero space dimensions). It gives the most basic example of the holographic correspondence for the string theory in one space dimension. This work is also important from this point of view.
2. Derivation of the entanglement entropy from the holographic correspondence The entanglement entropy is a useful concept for understanding the blackhole entropy from the microscopic point of view. Suppose that the space (at a fixed time) is divided into two subspaces A and B. The entanglement entropy measures the loss of information when the subspace B is not observable. In 2006, Dr. Takayanagi and his collaborator Dr. Ryu have calculated the entanglement entropy of conformal field theories through the gravitational dual in AdS3 space. As a result, they discovered that it is proportional to the area of the minimum surface in the AdS space whose endpoints are given by the boundary of the subspace A. This means that they have generalized the famous formula for the blackhole entropy to more general spacetime other than the blackhole. In recent years, the entanglement entropy has been extensively studied as a new order parameter in condensed matter physics. The scaling behavior they have found has received considerable attention.
3. Description of tachyon condensation by the string theory In the string theory, the system of brane-antibrane pair is unstable, since the open string connecting these two branes has a tachyonic mode. Dr. Takayanagi and his collaborators Dr. Terashima and Dr. Uesugi have exactly calculated the tachyon potential for this system by the description called boundary string field theory. Their result has been a foundation of the inflation models which use the tachyon condensation. Furthermore, Dr. Takayanagi has, in his work with Dr. Strominger, introduced the "time-like Liouville theory" obtained from the ordinary Liouville theory with the string worldsheet action by analytic continuation, as a method for handling the time-dependent background spacetime accompanied by tachyon condensation. This theory has also been a foundation of many subsequent works.
Despite his young age, Dr. Takayanagi has already made many outstanding achievements, and he is a leading researcher of the string-theory community in Japan. He will lead the field of the string theory internationally, and continue to play an active role in the future. He is the appropriate researcher for the Yukawa-Kimura prize this year.