Solving quantum field theories via curved spacetimes

Eleven years ago several theorists proposed a remarkable correspondence between two seemingly different kinds of theories. It is often called a duality because it is an equivalence between two different, "dual" descriptions of the same physics. On one side of the duality are certain quantum field theories (QFTs) - for example, Yang-Mills gauge theories similar to those in the standard model of particle physics. Such theories describe interacting particles moving in a flat d-dimensional spacetime. On the other side are theories that include gravity, like Albert Einstein's general relativity or its string-theoretic generalizations. The gravitational theories are defined in a higher-dimensional spacetime containing at least the d dimensions of the particle theory plus one extra dimension of infinite extent. They often include a number of finite dimensions - in the form of a sphere, for example. Depending on the context, the correspondence is known as a gauge/gravity duality, gauge/string duality, or AdS/CFT (anti-de Sitter/conformal field theory) correspondence. Do not despair if the terminology is unclear. In this article we will attempt to describe in simple terms what the duality is and how and why it is useful for studying a variety of problems.