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 pa rticular we probe subleading corrections to the difference c - a from the s tring-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-loo p R-2 and B boolean AND R boolean AND R terms in the low energy effective a ction. We identify these terms as coming from the R-4 terms. Similar consid erations 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 boolean AND F boo lean AND F should exist in the low energ 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. (C) 19 99 Elsevier Science B.V. All rights reserved.