A note on the chiral anomaly in the AdS/CFT correspondence and 1/N2 correction

According to the AdS/CFT correspondence, the d = 4, N = 4 SU(N) SYM is dual to the Type IIB string theory compactified on AdS(5) x S-5. A mechanism was proposed previously that the chiral anomaly of the gauge theory is accounted for to the leading order in N by the Chern-Simons action in the AdS(5) SUGRA. In this paper, we consider the SUGRA/string action at one loop and determine the quantum corrections to the Chern-Simons action. While gluon loops do not modify the coefficient of the Chern-Simons action, spinor loops shift the coefficient by an integer, We find that for finite N, the quantum corrections from the complete tower of Kaluza-Klein states reproduce exactly the desired shift N-2 --> N-2 - 1 Of the Chern-Simons coefficient, suggesting that this coefficient does not receive corrections from the other states of the string theory. We discuss why this is plausible. (C) 1999 Elsevier Science B.V. All rights reserved.