harvmac epsf

Robert de Mello Koch$^{1}$, Alastair Paulin-Campbell$^{2}$ and João P. Rodrigues$^{2}$

*Department of Physics,$^{1}$*

*Brown University*

*Providence RI, 02912, USA*

robert@het.brown.edu

*Department of Physics and Center for Nonlinear Studies,$^{2}$*

*University of the Witwatersrand,*

*Wits, 2050, South Africa*

paulin,joao@physnet.phys.wits.ac.za

We construct solutions of type IIB supergravity corresponding to $7$ branes, an $O7$ plane and 3 branes. By considering a probe moving in this background, with constant coupling and an AdS$_{5}$ component in its geometry, we are able to reproduce the exact low energy effective action for ${\cal N}=2$ super Yang-Mills theory with gauge group $SU(2)$ and $N_{f}=4$ massless flavors. After turning on a mass for the flavors we find corrections to the AdS$_{5}$ geometry. In addition, the coupling shows a power law dependence on the energy scale of the theory. The origin of the power law behaviour of the coupling is traced back to instanton corrections. Instanton corrections to the four derivative terms in the low energy effective action are correctly obtained from a probe analysis. We study how these instanton corrections are reflected in the background geometry by calculating the quark-antiquark potential. Finally we consider a solution corresponding to an asymptotically free field theory. Again, the leading form of 