Wilson loops in N = 4 gauge theory and fundamental strings in AdS(,5) x S('5)

The AdS/CFT correspondence is a duality between large N SU(N) gauge theory with N = 4 supersymmetry in 4 dimensions at strong coupling and type IIB string theory on AdS5 x S 5. According to the duality, Wilson loops are given by large fundamental strings in the AdS background. This dissertation examines various aspects of this relation.;There is a distinguished class of loops, which are the natural Wilson loop observables in this theory. The magnitude of their coupling to the gauge fields and the scalars is equal. We explore some of their properties, in particular, we show that their expectation values are free from ultra-violet divergence.;At strong coupling those Wilson loops can be evaluated by a saddle point expansion around classical solutions of string theory, or minimal surfaces. At the classical level we conclude that the action is not the area of the surface, which is divergent, but a Legendre transform of it.;At one loop in the worldsheet expansion, we develop a systematic approach to the study of semiclassical fluctuations of strings in AdS 5 x S5 based on the Green-Schwarz formalism. We show that the string partition function is well defined and finite, and issues related to different gauge choices are clarified.;We study four types of loops with different geometries. A single straight line is a BPS object and the corresponding Wilson loop is one. We show this in perturbation theory at weak coupling and to one loop order at strong coupling. A circular Wilson loop is similar to a straight line, but is not BPS, and it's expectation value is not one.;A particularly interesting observable is a pair of anti parallel lines. Those give the potential between two W-bosons. Another minimal surface we can find is for loops with cusps or intersections.;We also discuss the zig-zag symmetry of the loop operator. In the N = 4 gauge theory the zig-zag symmetry holds when the loop does not couple to the scalar fields. We show how this is realized by formal derivation and using the minimal surface calculation.;An important property of Wilson loops is that they solve the loop equations. We formulate the loop equation for the supersymmetric theory. We suggest two forms of the equation, one of them is particularly suited for the supersymmetric theory. The interesting thing about this loop equation is that it works on a restricted class of loops producing a closed equation. In bosonic theories it closes for straight light-like Wilson loops. In the N = 4 theory it closes exactly on all the special loops for which the AdS/CFT correspondence gives a simple prescription.;To the extent that we have checked, the minimal surface in AdS 5 x S5 gives a solution of both types of loop equations.