Holography, quantum entanglement and the emergence of spacetime

Arguably the most profound theoretical breakthough in the past 25 years has been the discovery of Holography. This by now strongly supported conjecture states a remarkable equivalence between gravity theories in certain spacetimes and lower-dimensional quantum field theories that can be thought of as living at the boundary of the gravitational spacetimes. Whilst this conjecture was originally formulated in a deductive (or top-down) manner in the context of string theory, it has now also been applied in an inductive (bottom-up) fashion to a wide range of physical systems including condensed matter systems, fluid mechanics, and the quark-gluon plasma created in heavy ion collisions.

An important question is how exactly the higher-dimensional gravitational spacetime is encoded in the lower-dimensional quantum field theory. Research of the last decade suggests that quantum entanglement plays a crucial role in this. In some cases, the relevant entanglement is between degrees of freedom in different spatial regions, but in other cases, most notably in matrix models, one also needs entanglement between “internal” degrees of freedom. Motivated by this, one aim of our research is to learn how to describe and compute entanglement between the degrees of freedom in systems of interacting matrices.

A specific question is how to decode what happens inside a black hole, and relatedly, how the Hawking radiation of an evaporating black hole contains information about the matter from which the black hole was formed. Recent progress suggests that entanglement plays a key role in this, and we are investigating possible ways in which radiation may or may not “know” about black hole interiors.