"When physicists study the quantum behavior of a system, we generally use an approach called mean (as in average) quantum field theory. This approach assumes that the system is mostly in the average state, with only small variations. It works well when the small variations don’t interact much; this is known as a weakly-coupled field theory. However, for many cases we care about, even small variations interact strongly with each other. One example is the strong nuclear force; another is high-temperature superconductors. Conventional techniques don’t work well for studying these “strongly-coupled” field theories. As we discuss below, holographic dualities provide a genuinely new approach to exploring these strongly-coupled systems.
A holographic duality is a map between a field theory in d dimensions, and a gravity theory in d+1 dimensions. In these maps, any physical quantity in the field theory has a dual in the gravitational theory, and vice versa. ""Dual"" means that a calculation in the field theory will always give the same answer as a calculation in the gravitational theory (and vice versa). We can thus choose to do the calculation wherever it is easiest. We use these maps in two ways: to understand strongly-coupled field theories, or to study gravity when quantum mechanics is important and spacetime is highly curved. Since quantum gravity is one of the great open questions of our time, developing a tool that helps us study it is of profound importance.
The first example, AdS-CFT duality, was found twenty years ago via string theory. AdS or Anti-de Sitter is the name of the gravitational theory, while the field theory behaves the same at any scale which means it is called a CFT or conformal field theory. This original duality has a few features that aren’t like our real world: it assumes supersymmetry (which we haven’t seen), and it assumes a large number of different charges (in the theory of the strong nuclear force, this number is only 3).
Physicists have proposed new holographic dualities in order to use them for realistic systems. In the last decade, there has been particular interest in building duals to non-relativistic systems, where space and time enter on fundamentally different footings, just as in the Schroedinger equation which has one time derivative but two space derivatives.
The first major goal of the research in this project was to “stress-test” the original AdS-CFT duality, by subjecting it to various alterations in order to understand if those changes broke the duality somehow. When a change succeeds, then we have a whole new forum where the tools of holographic duality can be applied; even when a change fails, we still learn something— instead we learn about how dualities themselves work.
The second major goal of this project was to develop a novel computational method, known as the quasinormal mode method (QNM), for studying quantum effects in gravitational systems such as the Anti-de Sitter space part of AdS-CFT. The QNM method relies on studying the vibrational modes of the spacetime as it relaxes after being perturbed. These relaxation modes are known as quasinormal modes, and their behavior can tell us a great deal about the quantum mechanical behavior and even the shape of the underlying space.
This project affects society as all physics does: we try to provide a greater understanding of the universe around us, so we can better predict its behavior as well as satisfy our curiosity. This research is fundamental in nature, improving the investigative tool of holographic dualities. Physicists have studied everything from quark gluon plasma to quantum gravity using this tool. The study of quantum gravity in general addresses our common call to understand the ""why"" and""how"" of our universe. Studies of the fundamental theories underlying nature serve this human urge to understand our world."
