In this thesis we investigate correlation functions in N=4 SYM.
The operator product expansion in N=4 SYM theory, as in any CFT, is
completely characterized by its 2-point and 3-point correlation
functions of local operators. In a first part of this thesis we
construct a new representation for two- and three-point correlators of
operators from sl(2) sector of planar N=4 SYM. The spin and twist of
operators are arbitrary. We start with the correlation function of
light-ray operators and carry out a projection to particular local
operators using the method of Separated Variables. With the same
calculation we obtain polynomials which are dual to wave functions of
In the second part of this thesis we focus our attention on the
particular case of twist-2 operators. We analyze the limit of large
spins as well as we calculate the so called "extremal correlator"
consisting of two twist-2 and one Konishi operator. It vanishes in the
lowest g^0 order and is computed at the leading g^2 approximation.
In the last part we generalize local operators of the leading twist-2
of N=4 SYM theory to the case of complex Lorentz spin j using
principal series representation of sl(2,R). We give the direct
computation of correlation function of two such non-local operators in
the BFKL regime when j-> 1. The correlator appears to have the
expected conformal coordinate dependence governed by the anomalous
dimension of twist-2 operator in NLO BFKL approximation predicted by
A.V.Kotikov and L.N.Lipatov.