Gravity duals of fractional branes in various dimensions

We derive type II supergravity solutions corresponding to space-filling regular and fractional Dp branes on (9-p)-dimensional conical transverse spaces. Fractional Dp-branes are wrapped D(p + 2)-branes; therefore, our solutions exist only if the base of the cone has a non-vanishing Betti number b₂. We also consider 11-dimensional SUGRA solutions corresponding to regular and fractional M2 branes on 8-dimensional cones whose base has a non-vanishing b₃. (In this case a fractional M2-brane is an M5-brane wrapped over a 3-cycle.) We discuss the gauge theory intepretation of these solutions, as well as of the solutions constructed by Cvetič and co-workers.