A CFT dual for evaporating black holes: boundary continuous matrix product states

Tensor network states, especially Matrix Product States (MPS), are crucial tools for studying how particles in large quantum systems are entangled with each other. MPS are particularly effective for modeling systems in one-dimensional space. Their continuous version, known as continuous Matrix Product States (cMPS), extends this approach to more complex quantum field theories that describe systems with an infinite number of interacting particles. This paper introduces a novel extension, boundary continuous Matrix Product States (BCMPS), which incorporate boundary states from conformal field theory (TFD state of two CFTs, let). We construct BCMPS and explore their potential holographic duals, linking them to black hole microstates with end-of-the-world branes in AdS/CFT. This connection hints at a deeper relationship between tensor networks and spacetime geometry, potentially offering new insights into the interplay between quantum information and gravity.