D-instanton probes of non-conformal geometries

D-instanton calculus has proved to be able to probe the AdS near horizon geometry for N D-branes systems which, when decoupled from gravity, yield four-dimensional superconformal gauge theories with various matter content. In this work we extend previous analysis to encompass fractional brane models which give rise to non-conformal N = 2 Super Yang-Mills theories. Via D-instanton calculus we study the geometry of such models for finite N and recover the beta function of the gauge coupling constants which is expected in non-conformal gauge theories. We also give a topological matrix theory formulation for the D-instanton action of these theories. Finally, we revisit the related system where the D3-branes wrap a R-4/Z(p) orbifold singularity and the D(-1)-branes are associated to instanton solutions of four-dimensional gauge theories in the blown down ALE space.