AdS/CFT, turbulence and chaos

Our current understanding of Nature is centered around two theories: general relativity which describes gravity, and quantum field theory which describes the strong and electroweak interactions and various low-energy phenomena. Naive attempts to unify these two theories lead to insurmountable difficulties. Moreover, a unified theory would ideally explain recent cosmological observations such as the acceleration of the universe, dark matter and cosmic inflation. This presents challenges to our understanding that must be addressed by new ideas.

As of today, the best candidate framework for unification is string theory which proposes that matter is not made of point particles, but one-dimensional strings. Although the theory solves the problem of combining gravity with the particle physics, the best understood solutions are ten dimensional. The extra six dimensions may be compactified which presents new challenges.

In the 1990s it has become clear that string theory also contains higher-dimensional objects called ``branes''. Furthermore, different types of string theory arise as limits of a unique theory: M-theory. It is known that in M-theory branes, and not strings, are the fundamental objects. However, a microscopic description of eleven-dimensional M-theory is still missing.

The Centre for Research in String Theory (CRST) at Queen Mary University of London has been at the forefront of research in string theory and quantum field theory. My STFC-funded research at CRST will be focused on the study of string theory. I will investigate two-dimensional toy models in order to unravel the mysteries of black holes in the context of quantum gravity.

Another research direction will be the study of extended objects (strings and branes) with the tools that I have recently developed. Understanding the quantum behavior of branes will be essential for understanding M-theory.

By perturbing strings, one can produce a very interesting phenomenon called wave-turbulence. In many respects, this phenomenon is similar to the fascinating (but more complicated) turbulence that can be observed in real-life fluids with unstable interacting vortices appearing on many scales. I will investigate wave-turbulence and develop analytical tools for describing the system.