2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/191459We 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.42 pages, harvmac, corrected typosHigh Energy Physics - Theorytext