  We describe the gravity duals of four-dimensional N=1 superconformal field
theories obtained by wrapping M5-branes on a punctured Riemann surface. The
internal geometry, normal to the AdS5 factor, generically preserves two U(1)s,
with generators (J+,J-), that are fibered over the Riemann surface. The metric
is governed by a single potential that satisfies a version of the Monge-Ampere
equation. The spectrum of N=1 punctures is given by the set of supersymmetric
sources of the potential that are localized on the Riemann surface and lead to
regular metrics near a puncture. We use this system to study a class of
punctures where the geometry near the sources corresponds to M-theory
description of D6-branes. These carry a natural (p,q) label associated to the
circle dual to the killing vector (p J+ + q J-) which shrinks near the source.
In the generic case the world volume of the D6-branes is AdS5 X S^2 and they
locally preserve N=2 supersymmetry. When p=-q, the shrinking circle is dual to
a flavor U(1). The metric in this case is non-degenerate only when there are
co-dimension one sources, M9-branes, obtained by smearing M5-branes that wrap
the AdS5 factor and the circle dual the superconformal R-symmetry. In the IIA
limit, they can interpreted as D8-branes. The D6-branes are extended along the
AdS5 and on cups that end on the co-dimension one branes. In the special case
when the shrinking circle is dual to the R-symmetry, the D6-branes are extended
along the AdS5 and wrap an auxiliary Riemann surface with an arbitrary genus.
When the Riemann surface is compact with constant curvature, the system is
governed by a Monge-Ampere equation.
