Form Factors, Integrability and the AdS/CFT Correspondence

Abstract

Form factors are matrix elements of local operators between scattering states, and are interesting off-shell objects in any QFT. In this thesis we will focus on the world-sheet theory describing strings in AdS5xS5, the Landau-Lifshitz model and a number of its generalizations. These theories are integrable, and a set of form factor axioms, essentially a set of consistency conditions, has been proposed for the world-sheet theory, though they have not yet been solved. Such a solution would be useful in understanding the interaction of strings in AdS5xS5 as the form factor axioms are closely related to those for the string interaction vertex.

Perturbative form factor calculations have been already carried out for the su(2) sector of the world-sheet string. One of the goals of the thesis is to extend the computation of the tree-level three-particle form factor to the full theory. We also study the Landau-Lifshitz model, a non-relativistic theory that can be obtained as a thermodynamic limit of the Heisenberg XXX spin chain, which is related to the dilatation operator in N=4 SYM and also emerges as a double limit of the AdS5xS5 string. Thus it is a useful tool in the context of the AdS/CFT correspondence. Moreover, its structure allows the perturbative computation of the S-matrix and the form factors to all loops. The other goal of this thesis is to compute all-loop form factors in the generalized LL model derived from the world-sheet string, and compare the findings to the known results for the corresponding spin chain at first-order in lambda.