Black Holes and Quark Confinement

Black Holes and Quark Confinement - SPECIAL SECTION Black...

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SPECIAL SECTION: CURRENT SCIENCE, VOL. 81, NO. 12, 25 DECEMBER 2001 1576 e-mail: [email protected] Black holes and quark confinement Edward Witten Department of Physics, Cal Tech, Pasadena, CA and CIT-USC Center For Theoretical Physics, USC, Los Angeles CA, USA Present address: Institute for Advanced Study, Princeton, NJ 08540, USA 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 ex- periments, 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 anti- quark 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 interac- tions. But unlike ordinary electric flux, the colour elec- tric 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 ever- growing flux tube. In practice, one never has enough energy to separate the quark and antiquark a macro- scopic distance, and that is why we never see an iso- lated quark or antiquark. The theoretical framework for analysing quark con- finement has been clear since 1973. It is the SU (3) gauge theory of the strong interactions, known as Quan- tum Chromodynamics or QCD. QCD is part of the stan- dard 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 undoubt- edly 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 stan- dard 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 ampli- tude W ( C ) for a quark to propagate around the loop C is exponentially small when the area is large,
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This note was uploaded on 02/07/2011 for the course PHYS 101 taught by Professor Aster during the Spring '11 term at East Tennessee State University.

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Black Holes and Quark Confinement - SPECIAL SECTION Black...

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