Research in the Particle Theory group
Integrability has proved to be a very powerful technique to understand and calculate the behaviour of a large class of quantum field theories. Originally, it was used to find the exact solution (in the sense of the spectrum, S-matrix, free energy and correlation functions) of QFTs in 1+1 dimensions. It is now recognised, however, that integrability is the key to understanding the fundamental structure of many systems, including string theory, the AdS/CFT correspondence and supersymmetric gauge theories.
Current work is focused on applying integrability techniques to the world-sheet theory of the string in the AdS/CFT correspondence. The fundamental idea here is that the world sheet theory of the string is actually a rather unconventional non-relativistic integrable QFT. The integrable structure allows for the exact solution of the energies of string states corresponding to anomalous dimensions in the dual gauge theory. This integrable QFT lies inside a much larger class including a rather novel supersymmetric relativistic QFT, and the exact S-matrix has been determined across this class. This suggests that the AdS/CFT correspondence itself can be deformed whilst maintaining all the key integrable properties.