The gauge/gravity correspondence is one of the most interesting conjectures in the string theory, which has attracted a great deal of attention in the last two decades. It states that there exist correspondences between gauge theories in N dimensions and gravitational theories in N+1 dimensions.
Besides its overwhelming evidences, this relationship has no formal mathematical proof so far. Dr. Nishimura and Dr. Hanada have tested this conjecture by developing a novel numerical method for the one-dimensional supersymmetric gauge theory. In particular, Dr. Nishimura and Dr. Hanada have achieved the verification for the case with the blackhole solutions, for which quantitative checks of the gauge/gravity correspondence have not been made.
The first example of the gauge/gravity correspondence is the AdS/CFT correspondence discovered by Maldacena in 1997. It is the equivalence between a supergravity on 5-dimensional Anti-de-Sitter (AdS) space and a conformal field theory (CFT) defined on the boundary of the AdS space. Dr. Nishimura and Dr. Hanada focused on the system with many D0 branes which describes blackhole solutions in supergravity. This is a generalized version of the AdS/CFT correspondence.
Dr. Nishimura and Dr. Hanada have, in their work with Dr. Anagnostopoulos and Dr. Takeuchi, developed a novel numerical method for the supersymmetric quantum theory (one-dimensional U(N) gauge theory with 16 supersymmetries), and checked the correspondence. In particular, they have calculated the internal energy at finite temperature numerically. They have demonstrated that the result is consistent with the high temperature expansion for small coupling constants, and it is also consistent with the blackhole solutions for large coupling constants, as is expected from the gauge/gravity correspondence.
Furthermore, Dr. Nishimura and Dr. Hanada have, in their work with Dr. Takeuchi and Dr. Hyakutake, shown that the corrections by the string oscillation are calculable by the same method. In their paper with Dr. Ishiki and Dr. Hyakutake published in Science, they have shown that the 1/N corrections for the internal energy are consistent with the corrections by the quantum-gravity effect motivated by the string theory. They have also studied the consistencies in the correlation functions in their work with Dr. Sekino and Dr. Yoneya
With these outstanding results, Dr. Nishimura and Dr. Hanada have made great achievements not only in the development of the numerical method in supersymmetric gauge theories, but also in the verification of the gauge/gravity correspondence. It should be also highly praised that they have introduced a new approach --- the numerical method in the gauge theory --- into the research area of the gauge/gravity correspondence, and verified its efficiency. In the future, further developments will be made by this method.