|
Public viva-voce Notification Date: Tuesday, 2 September 2025 Time: 2:00 PM Venue: Seminar Hall Cosmologies, singularities, quantum extremal surfaces, holographic complexity, and time entanglement and pseudo-entropy. Hitesh Kumar Saini Chennai Mathematical Institute. 02-09-25 Abstract
Recent developments in quantum information theory—particularly the concepts of complexity and entanglement—are shedding new light on the structure of spacetime in holography In the first part of this talk, we examine how these probes behave in time-dependent and singular spacetimes, with a focus on cosmological geometries featuring Big-Crunch singularities. In particular, we study holographic volume complexity and entanglement entropy in singular settings such as AdS Kasner, hyperscaling-violating Kasner, and Lifshitz Kasner spacetimes. By extremizing codimension-one bulk volumes, we find that complexity surfaces universally avoid the singularity, shifting from spacelike near the boundary to lightlike deep in the bulk. Complexity vanishes as the crunch is approached, suggesting a low-complexity state in the dual field theory. The scaling behavior depends on geometry: linear growth in AdS and isotropic Lifshitz, versus nonlinear trends in hyperscaling-violating cases. Entanglement entropy shows similar infrared features. The second part turns to time entanglement and pseudo-entropy, concepts motivated by de Sitter holography and defined via the time evolution operator. We identify conditions under which timelike entanglement entropy is real and show that, for time-independent interactions, it matches thermal entanglement at an imaginary temperature. Projecting the time evolution operator onto an initial state yields an entropy matching pseudo-entropy from transition matrices. We also explore time-dependent interactions, which produce more intricate time entanglement structures without straightforward analytic continuation. Together, these results deepen our understanding of complexity and entanglement in dynamical and singular spacetimes, advancing the dialogue between quantum information and holography.
|
