According to the AdS/CFT duality a remarkable correspondence exists between strings in AdS and operators in N=4 SYM. A particularly important case is that of folded strings and the so called twist-operators in gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability. In this talk I will show how to match the expression of the anomalous dimension of twist operators (cusp anomaly) as computed in string theory with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability. I will also comment on the computation of finite size corrections to the cusp anomaly.

According to AdS/CFT a remarkable correspondence exists between strings in AdS5 x S5 and operators in N=4 SYM. A particularly important case is that of fast-spinning folded closed strings and the so called twist-operators in the gauge theory. This is a remarkable tool for uncovering and checking the detailed structure of the AdS/CFT correspondence and its integrability properties. In this talk I will show how to match the expression of the anomalous dimension of twist operators as computed from the quantum superstring with the result obtained from the Bethe ansatz of SYM. This agreement resolves a long-standing disagreement between gauge and string sides of the AdS/CFT duality and provides a highly nontrivial strong coupling test of SYM integrability.

In this talk, I will discuss a new family of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere in space-time and generically preserve two super-conformal charges. On the string side, via AdS/CFT duality, these loops map to surfaces which are 'pseudo-holomorphic' with respect to a novel almost-complex structure defined on a suitable subspace of AdS5xS5. Of particular interest is the subclass of loops lying on a two-sphere in space-time whose expectation value is conjectured to be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2. Several evidences for this conjecture, both on the gauge theory and on the string theory side will be discussed.

In this talk, I will discuss a new family of supersymmetric Wilson loop operators in N=4 SYM. These operators can be defined for any loop on a three-sphere in space-time and generically preserve two super-conformal charges. On the string side, via AdS/CFT duality, these loops map to surfaces which are 'pseudo-holomorphic' with respect to a novel almost-complex structure defined on a suitable subspace of AdS5xS5. Of particular interest is the subclass of loops lying on a two-sphere in space-time whose expectation value is conjectured to be computed exactly in terms of the analogous observables in bosonic 2d Yang-Mills on S2. Several evidences for this conjecture, both on the gauge theory and on the string theory side will be discussed.

In this talk we discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. We will see that combining T-duality along four directions in Poincare parametrization of AdS5 with a similar duality transformation on some of the fermionic variables maps the superstring action into itself. One implication is that, after duality, the superstring has a 'dual' superconformal symmetry group. Furthermore this dual superconformal symmetry can be seen as a consequence of the integrability of the superstring. This will also suggest that the dual superconformal charges correspond to non-local charges of the original model before T-duality.