Correlation functions - our main goals


  • Weak coupling: Derivation of general expressions for three-point functions at weak coupling with the help of the Algebraic Bethe Ansatz.

At tree level the computation of the three-point functions can be reformulated in terms of spin chains as a cut-and-paste procedure, similar to the one used in string field theory to construct a three-string vertex. This analogy to string theory is very suggestive, but so far qualitative. Much has to be done to make contact with the real string theory in AdS5 xS5. We expect that the methods of integrability will be useful in calculating correlation functions.


  • Strong coupling: Calculation of correlation functions at strong coupling with the help of the classical inverse scattering methods in string theory.

The problem of calculating the correlation functions in classical string theory at strong coupling is well-posed but difficult to solve. It boils down to finding classical solutions in the sigma-model with prescribed boundary conditions that correspond to the insertions of vertex operators. There is no systematic method to construct vertex operators for string theory in AdS5x S5. While the energy levels of the string are eigenvalues of the dilatation operator (the string Hamiltonian in the light-cone gauge), the vertex operators should be related to its eigenfunctions. Making this relationship precise will allow us to make a direct contact with integrability and understand how
spin chains arise in the AdS/CFT correspondence.


  • Any coupling: Development of new non-perturbative methods to compute correlation functions in N = 4 SYM theory at any coupling.