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 R and B ∧R∧R terms in the low energy effective action. We identify these terms as coming from the R 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) term is leading for the N = 1 CFT and it is indeed present in the N = 2 five-dimensional supergravity.