We explore subleading contributions to the two basic central charges c and a
of four-dimensional conformal field theories in the AdS/CFT scheme. In
particular we probe subleading corrections to the difference c-a from the
string-theory side. In the N=4 CFT, c-a vanish identically consistently with
the string-theory expectations. However, for N=1 and N=2 CFTs, the U_R(1)
anomaly, which is proportional to c-a, is subleading in the large N limit for
theories in the AdS/CFT context and one expects string one-loop R^2 and B
\wedge R \wedge R terms in the low energy effective action. We identify these
terms as coming from the R^4 terms. Similar considerations apply to the
U_R(1)^3 anomaly which is, however, subleading only for N=2 theories. As a
result, a string one-loop term B \wedge F \wedge F should exist in the low
energy effective action of the N=4 five-dimensional supergravity. The U_R(1)^3
term is leading for the N=1 CFT and it is indeed present in the N=2
five-dimensional supergravity.Comment: 15 page
