Black holes and quark confinement

MOST expositions of string theory focus on its possible use as a framework for unifying the forces of nature. But I will take a different tack in this article. Rather than the unification of the forces, I will here describe what one might call the unification of the ideas. Let us begin with the classic and not fully solved problem of ‘quark confinement’. From a variety of experiments, physicists learned roughly 30 years ago that protons, neutrons, pions, and other strongly interacting particles are made from quarks (and antiquarks, and gluons). But we never see an isolated quark. It is believed that if one tries to separate a quark– antiquark pair in, say, a pion, the energy required grows linearly with the distance between the quark and antiquark due to the formation of a ‘colour electric flux tube’ (Figure 1). The idea is that a quark or antiquark is a source or sink of ‘colour electric flux,’ which is the analog of ordinary electric flux for the strong interactions. But unlike ordinary electric flux, the colour electric flux is expelled from the vacuum and is trapped in a thin ‘flux tube’ connecting the quark and antiquark. This is very similar to the way that a superconductor expels ordinary magnetic flux and traps it in thin tubes called Abrikosov–Gorkov vortex lines. As a result, to separate a quark and antiquark by a distance R takes an energy that keeps growing as R is increased, because of the energy stored in the evergrowing flux tube. In practice, one never has enough energy to separate the quark and antiquark a macroscopic distance, and that is why we never see an isolated quark or antiquark. The theoretical framework for analysing quark confinement has been clear since 1973. It is the SU(3) gauge theory of the strong interactions, known as Quantum Chromodynamics or QCD. QCD is part of the standard model of particle physics, in which all of the known forces of nature except gravity are described by gauge theories. The simplest gauge theory is undoubtedly Maxwell’s theory of the electromagnetic field. QCD, which is used to describe the strong interactions or nuclear forces, is the most difficult part of the standard model. QCD offers a clear framework in principle to address the question of quark confinement, but the mathematics required has been too difficult. To test for confinement, one looks at a quark propagating around a large loop C in space–time (Figure 2). Let A(C) be the area of a soap bubble of minimal area whose boundary is C. Quark confinement occurs if the probability amplitude W(C) for a quark to propagate around the loop C is exponentially small when the area is large,