RG fixed points in supergravity duals of 4-d field theory and asymptotically AdS spaces

Recently, it has been conjectured that supergravity solutions with two asymptotically AdS5 regions describe the RG flow of a 4-d field theory from a UV fixed point to an interacting IR fixed point. In this paper we lend support to this conjecture by showing that, in the UV (IR) limit, the two-point function of a minimally coupled scalar field depends only on the UV (IR) region of the metric, asymptotic to AdS5. This result is consistent with the interpretation of the radial coordinate of Anti de Sitter space as an energy scale, and it may provide an analog of the Callan–Symanzik equation for supergravity duals of strongly coupled field theories.