Domain walls of D = 5 supergravity and fixed points 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) AdS5 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 multiplets, but not to scalars from hypermultiplets. We discuss the c-theorem, the β-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 orientifold construction for an elliptically fibered CY with F_1 basis (corresponding to N=1 SYM)