As a postdoctoral researcher, he was at the Kavli Institute for Theoretical Physics until 2008, where he worked with Tadashi Takayanagi.
His theoretical work involves solid-state systems in which quantum mechanical and topological phenomena play a special role.
Ryū is known for a 2006 paper with Tadashi Takayanagi, later known as the Ryu–Takayanagi conjecture, in which they calculated the entropy from quantum entanglement in conformal field theory via the Bekenstein-Hawking entropy of black holes in the context of Juan Maldacena's holographic principle and conformal field theories on a surface correspond to a gravitational theory in the enclosed volume.
This also has applications in solid-state physics, since conformal field theories also play a role in many systems at the critical point.
In 2024 he was again awarded the Dirac Medal of the ICTP together with Tadashi Takayanagi, Horacio Casini and Marina Huerta.