Our group actively studies the longstanding puzzle of how information is preserved in black hole evaporation. A central focus is on understanding the Page curve—the entanglement entropy of Hawking radiation over time—and how the island formula has recently been invoked to reconcile semiclassical gravity with quantum unitarity. We explore both Euclidean path integral approaches and modern insights from quantum information, such as the Hayden–Preskill recovery protocol. In addition, we examine the spectral form factor as a diagnostic of quantum chaos and the fine-grained structure of black hole microstates, aiming to connect quantum gravity with random matrix theory.

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Another line of research delves into the operators behind the horizon—often referred to as “mirror operators” in the context of Tomita-Takesaki modular theory—and the broader question of whether effective field theory can be consistently extended into the interior. We investigate how degrees of freedom deep inside the black hole horizon may be encoded on boundary, guided by the principle of black hole complementarity and related frameworks like the AdS/CFT correspondence. Through this lens, we aim to clarify the nature of the black hole interior, bridging the gap between macroscopic semiclassical descriptions and the underlying quantum-mechanical laws that ensure unitary evolution.