Domain walls of D=5 supergravity and fixpoints of N=1 Super Yang Mills

Employing the AdS/CFT correspondence, we give an explicit supergravity picture for the renormalization group flow of couplings 4-d super Yang Mills with four supercharges. The solution represents a domain wall of 5-d, N=2 supergravity, that interpolates between two (different) $AdS_5$ vacua and is obtained by gauging a U(1) subgroup of the SU(2) R-symmetry. On the supergravity side the domain wall couples only to scalar fields from vector mulitplets, but not to scalars from hyper multiplets. We discuss the c-theorem, the $\beta$-functions and consider two examples: one is the sugra solution related to $Z_k$ orbifolds (corresponding to N=2 SYM) and the other is an orientfold construction for an elliptically fibered CY with $F_1$ basis (corresponding to N=1 SYM).