Some of my current research interests

Introduction

The theory contains quarks and gluons as its fundamental particles but, paradoxically, these do not appear as stable (or even unstable) particles in the real world. Instead what one observes experimentally are protons, pions, rho-mesons etc. All this is in contrast to Quantum Electrodynamics (QED), the well-understood quantum theory of electromagnetism, where electrons, photons, etc are the fundamental particles and these do appear as particles in the real world (e.g. electric current, light).

Thus a perturbation expansion (the very successful analytic technique for calculating the properties of QED) is not going to be useful for attacking most of the questions in QCD. After all, the perturbative approach starts by assuming that the easily-solved free theory is some kind of reasonable first approximation to the full theory and then adds the effects of interactions as a perturbation around the free theory. This makes sense in QED where electromagnetism does indeed look like free electrons and photons to a crude first approximation. However there is no sense in which protons, pions etc resemble a world of free quarks and gluons.

To address some of the most interesting problems in QCD, such as the confinement of quarks and gluons, the spontaneous breaking of chiral symmetry, and the details of the mass spectrum, numerical techniques have been developed where one discretises space-time, defines QCD on the resulting lattice of space-time points ("Lattice QCD") and simulates the theory using a computer. Much of my research has involves the use of such techniques. For an introduction see my lectures at Erice 2002.

QCD is based on an SU(3) gauge theory. One can imagine extending this to an arbitrary SU(N) gauge group and one can then try to solve that by perturbing in 1/N around N=oo colours. This is `t Hooft's imaginative alternative to trying to perturb in the coupling around the free field theory. The SU(oo) theory is very much simpler than SU(3), while not simple enough to be analytically tractable, and has become the point of convergence of various theoretical approaches -- in particular in the dual string framework. At the same time there have been serious attempts to determine the properties of this theory numerically -- see my recent talk at Large N 2004.

Some problems I have been recently working on

• SU(N) gauge theories for all N e.g.
• large N effective string theory e.g.
• k-strings e.g.
• instantons and chiral symmetry breaking e.g.
• topology and the eta-prime mass in QCD e.g.
• glueballs and the Pomeron e.g.
• deconfinement e.g.