  We construct a new class of supersymmetric surface operators in N=4 SYM and
find the corresponding dual supergravity solutions. We show that the insertion
of the surface operator - which is given by a WZW model supported on the
surface - appears by integrating out the localized degrees of freedom along the
surface which arise microscopically from a D3/D7 brane intersection.
Consistency requires constructing N=4 SYM in the D7 supergravity background and
not in flat space. This enlarges the class of holographic gauge theories dual
to string theory backgrounds to gauge theories in non-trivial supergravity
backgrounds. The dual Type IIB supergravity solutions we find reveal - among
other features - that the holographic dual gauge theory does indeed live in the
D7-brane background.
