The 2017 Yukawa-Kimura Prize:
Dr. Hiroshi Suzuki for his research on the study of gradient flow and energy momentum tensor in lattice gauge theory

Lattice gauge theory, gauge theories on a spacetime that is discretized into a lattice, has been the most powerful method to analyze the dynamics of the strong interaction. In recent years, a method called "Yang-Mills gradient flow" has attracted much attention. In this method, the field operators flow as a "virtual time" goes, and its "time" evolution is governed by a kind of diffusion equation whose source term involves a gradient of the classical action. M. Luscher and P. Weisz have shown that any correlation function of such flowing operators remain finite at all orders of the perturbation theory, which means that the operators generated by this method are physical quantities, being independent of methods of the regularization and the renormalization. Since this method allows one to calculate physical quantities which have well-defined continuum limits in lattice gauge theory, the method is expected to be applicable to complicated problems such as electroweak processes between hadrons, the analysis of the static and the dynamical properties of quark-gluon systems at finite temperature, and so on. A connection to the Wilsonian renormalization group has been also discussed.

Dr. Suzuki has established a method for applying the Yang-Mills gradient flow to the formulation of the physical quantities defined by the energy-momentum tensor. That is, he has calculated the asymptotic expansion coefficients which relate the original renormalized energy momentum tensor operators to the short-flowed operators. As a result, he has derived a universal formula of the renormalized operator for the energy-momentum tensor [1]. Furthermore, in his work with Hiroki Makino, he has developed the formulation to the systems which include fermionic fields [2].

Energy-momentum tensor is one of the most fundamental physical quantities in field theories. It is the Neother current associated with the translational invariance of the system, and it carries physical information (energy, momentum, angular momentum, pressure, stress, viscosity, heat capacity, renormalization group functions, etc.) on the spacetime symmetry. In the lattice gauge theories, however, the translational invariance is apparently broken in the first place, and the construction of energy-momentum tensor has been a quite nontrivial and challenging task for long time. The achievement by Dr. Suzuki can make us overcome this difficulty since his works provide a universal closed formula for the energy-momentum tensor which does not depend on the regularizations. In fact, Masayuki Asakawa, Tetsuo Hatsuda, Etsuko Itoh, Masakiyo Kitazawa and Takumi Irie, et. al have immediately applied his works to QCD at finite temperature [3], and they have shown that this approach is promising. We can expected that, if it works well, vital information to understand neutron starts and heavy ion collisions will be obtained. It should be also emphasized that the work by Dr. Suzuki provides a universal formula of the energy-momentum tensor, which means that his work is important not only in the lattice gauge theories but also in more general context of theoretical physics. His achievement is appropriate for Yukawa-Kimura prize for its significant interest, importance and applicability in quantum field theory.

Besides this work, Dr. Suzuki has made many brilliant achievements over a wide range of themes in theoretical physics, playing a leading role in the study of quantum filed theory as one of the representative theoretical physicist in Japan. He is very appropriate for the researcher who deserves Yukawa-Kimura prize.

[1] H. Suzuki, "Energy-momentum tensor from the Yang-Mills gradient flow", PTEP 2013 083B03.

[2] H. Makino and H.Suzuki, "Lattice energy-momentum tensor from the Yang-Mills gradient flow-inclusion of fermion fields", PTEP 2014 063B02.

[3] M. Asakawa, T.Hatsuda, E.Ito, M.Kitazawa and H. Suzuki, "Thermodynamics of SU(3) gauge theory from gradient flow on the lattice", Phys. Rev. D90 (2014) no.1, 011501, Erratum: Phys. Rev. D92 (2015) no.5, 059902.