Dr. Dmitri V. Fursaev, JINR, Dubna

Entaglement in quantum gravity and the plateau problem

Quantum entanglement is an important physical phenomenon when quantum states of different objects cannot be described independently even if the objects are spatially separated. The aim of the talk is the entropy of entanglement between microscopic states in a quantum gravity theory which are separated by a hypersurface. We present arguments that: 1) the entanglement entropy can be determined as macroscopical quantity without knowing the real microscopical content of the fundamental theory; 2) when the system is separated by a minimal hypersurface the entropy has the same form as the Bekenstein-Hawking entropy of a black hole. The relation between the entropy and the theory of minimal surfaces (the Plateau problem) is in a remarkable accord with the basic features of the von Neumann entropy, such as subadditivity property. Another evidence in its favor comes from a “holographic formula” recently established for QFT models which admits a description in terms of an anti-de Sitter (AdS) gravity one dimension higher. The holographic formula enables one to express the entanglement entropy in these models in terms of the area of a minimal surface in the AdS bulk. The topics covered in the talk include: properties of the entanglement entropy, entanglement in many–body systems and in QFT, entanglement in quantum gravity, the holographic formula and its applications to strongly coupled gauge theories