The 2021 Yukawa-Kimura Prize:
Dr. Tatsuma Nishioka for his research on "Studies of various entropies in quantum field theory and gravity theory"

Holographic duality has been an important research topic in quantum field theory based on superstring theory and quantum gravity for more than 20 years, and has been actively studied by many researchers. Holographic duality refers to a remarkable property that a quantum field theory without gravity and a theory with gravity are equivalent quantum mechanically. In particular, in the case of conformal field theory (CFT), the spacetime of the corresponding gravitational theory becomes asymptotically anti-de Sitter (AdS), hence it is called AdS/CFT correspondence. This holographic duality is widely accepted because there are huge amount of non-trivial evidence. However, since the underlying principle is not yet well-understood, it is important to analyze the quantum field theory side and the gravity theory side independently and verify whether they are consistent with the predictions of holographic duality. In recent years, in addition to the usual entropy, the entanglement entropy, which measures the degree of quantum entanglement, and its extension, such as Renyi entropy, used in quantum information theory, have attracted much attention, because they provide evidence of the holographic duality and clues toward the understanding of its principle. Dr. Nishioka has done a lot of excellent research in this topic, among which the following three works are outstanding.

1. Supersymmetric Renyi Entropy

Dr. Nishioka, in collaboration with Dr. Yaakov, proposed a new information measure called "supersymmetric Renyi entropy", which is a natural extension of the Renyi entropy for supersymmetric theories, and found that it can be computed analytically in three-dimensional superconformal gauge theories (Ref.[1]). The usual Renyi entropy is generally very difficult to calculate in interacting quantum field theories in three or more dimensions. The finding that the supersymmetric Renyi entropy can be computed exactly is a remarkable achievement. Furthermore, Dr. Nishioka found that this quantity can be calculated exactly not only in the gauge theory but also in its holographic dual, and showed that it is useful for the purpose of testing the AdS/CFT correspondence (Ref.[2]).

2. Entanglement entropy in theories with a mass gap (Ref.[3])

Dr. Nishioka has also made notable contributions to the study of entanglement entropy for theories with a mass gap and broken conformal symmetry. He, together with Dr. Klebanov, Dr. Pufu, and Dr. Safdi, clarified how entanglement entropy depends on the shape of the region specified in its definition and the mass. He also provided a concrete evidence of F-theorem, which is a conjecture that a quantity representing the effective degrees of freedom, defined using entanglement entropy, decreases monotonically as one goes to lower energies along the renormalization group flow. Furthermore, He performed the analysis in both quantum field theory and its holographic dual description, and showed that they are consistent with each other.

3. A two-dimensional conformal field theory description of the black hole entropy. (Ref.[4])

Dr. Nishioka, in collaboration with Dr. Hartman, Dr. Murata and Dr. Strominger, found a duality between the extremal Kerr-Newman-AdS/dS black hole and two-dimensional chiral conformal field theory, and showed that the entropy of this black hole can be derived from microscopic calculations in conformal field theory. This work is a major generalization of the Kerr/CFT correspondence, which is a duality between extremal rotating black holes and two-dimensional chiral conformal field theories. This is a pioneering work that proposed a holographic duality with spacetimes that are not asymptotically AdS assumed in the usual AdS/CFT correspondence.

Dr. Nishioka has also made many other outstanding achievements and continues to be active as a leading expert in this field. For these reasons, he deserves to be a recipient of the Yukawa-Kimura prize.