  In N=2 superconformal field theories the Kahler potential is known to be tree
level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of
supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections
to the Kahler potential. We analyse the two-loop corrections on the Coulomb
branch for a complex deformation. For an arbitrary chiral field in the Cartan
subalgebra we reduce the problem of computing the two-loop Kahler potential to
that of diagonalising the mass matrix, we then present the result in a
manifestly superconformal form. The mass matrix diagonalisation is performed
for the case of the chiral background that induces the breaking pattern SU(N)
-> SU(N-2)*U(1)^2. Then, for the gauge group SU(3), the Kahler potential is
explicitly computed to the two-loop order.
