Supersymmetric Wilson loops in the AdS/CFT correspondence

Abstract

Our modern understanding of the fundamental interactions of Nature, with the sole exception of gravity, is based on a symmetry principle known as "gauge symmetry". Quantum chromodynamics (QCD), the theory which describes the interaction of quarks and gluons inside of atomic nuclei, is one of the most notable examples of a theory with such a symmetry. A feature of QCD is that, unlike what happens with other particles such as electrons or photons, we are not able to see directly quarks and gluons because of a property known as "color confinement": the attractive coupling between quarks and gluons becomes strong as we try to separate them and all we can see are color neutral states. Understanding confinement is one of the most important and challenging tasks in theoretical and mathematical physics - it is in fact one of the Clay Institute Millennium Prize Problems, whose solutions are worth 1 million dollars each! In this task it is of central importance the study of gauge theory operators known as "Wilson loops". These operators represent the phase factor associated to charged particles moving along some contour and can probe the forces acting on such particles. In particular, theories exhibiting confinement have Wilson loops with expectation values that scale like the area of the contour swept by the particles.Recently, string theory has given us a novel and extremely powerful tool to address the study of confinement and strongly coupled gauge theories: the AdS/CFT (or "gauge/string") correspondence. This correspondence allows to map a gauge theory to a theory of strings living in some appropriate space, and to reformulate questions in the gauge theory in terms of equivalent questions in the string theory. This is useful because, sometimes, difficult problems on one side of the correspondence become tractable on the other side. In particular, the Wilson loops of the gauge theory can be described in the dual string picture in terms of surfaces with boundaries. This dual description has allowed, in the past few years, to achieve substantial progress in the study of these operators.The proposal for this master thesis is to review some aspects of this recent progress, both on the gauge theory side and on the string theory side of the AdS/CFT correspondence, and also to carry out some simple original computations. (AU)