A note on correlation functions in AdS5/SYM4 correspondence on the Coulomb branch

We compute certain two-point functions in D = 4, N = 4, SU(N) SYM theory on the Coulomb branch using SUGRA/SYM duality and find an infinite set of first order poles at masses of order (Higgs scale)/(gY M √ N). 1 E-mail: [email protected] 2 E-mail: [email protected] 1. Apart from being a universal way of looking at the gravity/gauge theory relation, Maldacena’s supergravity(SUGRA)/super Yang-Mills(SYM) duality [1, 2] provides a useful tool for the study of strongly coupled gauge theories. The precise rules for relating SUGRA and SYM observables in the context of AdS5/CFT4 duality of ref.[1] were given in refs.[4, 5]. They consist of (A) the dictionary between gauge-invariant SYM operators and SUGRA fields, and (B) the precise relation between the generating functional of correlators of N = 4 CFT4 and the Type IIB SUGRA action S(φ) evaluated on the solutions φ of the classical equations satisfying the boundary conditions φ|∂AdS ∼ φ0, where φ0 are the sources for the operators of CFT4.