N=1 super-Yang–Mills renormalization schemes for fractional branes

We investigate N=1 super-Yang–Mills theory using fractional branes. We first define the β-function with respect to a supergravity coordinate. To provide the relation between the supergravity parameter and the renormalization group scale we use the UV known gauge theory β-function as a type of boundary condition. We show that there are no privileged renormalization schemes connected to a given supergravity solution while we investigate in some detail two schemes. The Wilsonian one where just one loop is manifest and the one containing multi-loops. A new functional relation between the gaugino condensate and the supergravity coordinates is finally determined.