Gravity describes large, heavy objects like planets, galaxies and black holes. Quantum mechanics describes small, fuzzy things like electrons orbiting the nucleus, or cats trapped in radioactive boxes. But if we add many of these small fuzzy things together, they must be described by both gravity and quantum mechanics. Because gravity and quantum mechanics usually apply to such radically different domains, they are hard to reconcile, and a combined theory of quantum gravity is one of the holy grails of theoretical physics.
Although quantum gravity in full generality remains mysterious, we have a simple but miraculous example called the AdS/CFT correspondence. It tells us that quantum gravity in a special (d+1)-dimensional spacetime (Anti-de Sitter = AdS) is exactly equivalent to quantum mechanics in d dimensions (conformal field theory = CFT). For instance, a 3D black hole can be run on a 2D quantum computer! Although this change in dimension (d + 1 → d) seems impossible, it is actually expected as a general feature of quantum gravity, and in AdS/CFT it is realised in a beautiful way: the CFT system lives on the boundary of AdS spacetime.
AdS/CFT is a gift that keeps on giving. It helps us approach deep questions in quantum gravity, like: what goes on inside a black hole? and what is spacetime anyway? But as we twiddle knobs in the correspondence, we end up getting new and surprising insights into classical gravity. And because classical gravity calculations are easier than quantum ones, we can use AdS/CFT to sneakily do our quantum mechanics homework!
AdS/CFT is still far from understood, with many active research frontiers. At the moment, I’m interested in two related questions:
- What can AdS/CFT tell us about black holes and physics behind the horizon?
- What happens if we add boundaries to the quantum mechanical (CFT) system?
The first question is obviously interesting because black holes are cool and weird and confusing. The second question sounds technical, but turns out to be related to the first: adding a boundary often provides simple, tractable models of puzzling aspects of black hole physics. So by answering the second question, we get technical tools which help us with the first!