# Correlation functions in N=4 SYM Evgeny Sobko (LPT)

### Abstract

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
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
sl(2,R) spin-chain.
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.