  We determine the one-loop deformation of the conformal symmetry of a general
N}=2 superconformally invariant Yang-Mills theory. The deformation is computed
for several explicit examples which have a realization as world-volume theories
on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N),
USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the
traceless antisymmetric representation and four hypermultiplets in the
fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two
hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N).
The existence of quantum corrections to the conformal transformations imposes
restrictions on the effective action which we study on a subset of the Coulomb
branch corresponding to the separation of one brane from the stack. In the N=4
case, the one-loop corrected transformations provide a realization of the
conformal algebra; this deformation is shown to be one-loop exact. For the
other two models, higher-loop corrections are necessary to close the algebra.
Requiring closure, we infer the two-loop conformal deformation.
