Conference

In this talk we give a survey of recent developments concerning the fermionic structure in the sine-Gordon model. For the lattice counterpart (6 vertex model), we introduce fermions acting on the space of (quasi) local operators. The main theorem is a determinant formula for the expectation values of fermionic descendants of primary fields. In the continuum limit this construction gives rise to a basis of the space of all descendant fields, whose expectation values take a very simple form. Unexpectedly, it turns out that the action of our fermions on form factors coincides with yet another fermions which have been introduced some time ago by Babelon, Bernard and Smirnov.

For N=4 super Yang-Mills theory, in the large-N limit and at strong coupling, Wilson loops can be computed using the AdS/CFT correspondence. In the case of flat Euclidean loops the dual computation consists in finding minimal area surfaces in Euclidean AdS3 space. In such case very few solutions were known. In this talk I will describe an infinite parameter family of minimal area surfaces that can be described analytically using Riemann Theta functions. Furthermore, for each Wilson loop a one parameter family of deformations that preserve the area can be exhibited explicitly. The area is given by a one dimensional integral over the world-sheet boundary.

We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation.

In this talk I will report on the computation at strong coupling of the AdS contribution to the 3-point correlation function of operators corresponding to classical strings which rotate in the S5. This contribution is universal for all operators which have only SO(6) charges.