Subleading corrections and central charges in the AdS/CFT correspondence

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 UR(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 R2 and B∧R∧R terms in the low energy effective action. We identify these terms as coming from the R4 terms. Similar considerations apply to the UR(1)3 anomaly which is, however, subleading only for N=2 theories. As a result, a string one-loop term B∧F∧F should exist in the low energy effective action of the N=4 five-dimensional supergravity. The UR(1)3 term is leading for the N=1 CFT and it is indeed present in the N=2 five-dimensional supergravity.