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

TL;DR

This paper uses the AdS/CFT correspondence to model the renormalization group flow of 4-dimensional super Yang-Mills theories with four supercharges through a supergravity domain wall solution that interpolates between two AdS_5 vacua.

Contribution

It provides an explicit supergravity domain wall solution for RG flows in N=1 and N=2 super Yang-Mills theories, connecting different AdS_5 vacua via gauged supergravity.

Findings

Constructed supergravity solutions for RG flows in N=1 and N=2 SYM.

Analyzed the c-theorem and beta-functions in these flows.

Related solutions to orbifold and orientifold string constructions.

Abstract

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 orientifold construction for an elliptically fibered CY with F_1 basis (corresponding to N=1 SYM).