AdS/CFT four-point functions: How to succeed at z-integrals without reallytrying

A new method is discussed which vastly simplifies one of the two integrals over AdS(d+1), required to compute exchange graphs for four-point functions of scalars in the AdS/CFT correspondence. The explicit form of the bulk-to -bulk propagator is not required. Previous results for scalar, gauge boson and graviton exchange are reproduced, and new results are given for massive vectors, It is found that precisely for the cases that occur in the AdS(5) x S-5 compactification of Type IIB supergravity, the exchange diagrams red uce to a finite sum of graphs with quartic scalar vertices, The analogous i ntegrals in n-point scalar diagrams for n > 4 are also evaluated. (C) 1999 Elsevier Science B.V. All rights reserved.