Breaking SUSY in AdS / CFT

We study various two-point functions in certain defect versions of \( \mathcal{N} = 4 \) super Yang Mills theory. These defect theories are obtained by insertion of a D7 probe-brane, with either \( AdS_4 \times S^2 \times S^2 \) or \( AdS_4 \times S^4 \) geometry, into the standard D3 brane configura- tion of AdS / CFT. The \( \mathcal{N} = 4 \) SYM theories, arising from the decoupling limit of these brane configurations, have non-zero vacuum expectation values (vevs) for the scalar fields \( \phi_i \). These non-zero vevs breaks super symmetry completely and conformal sym- metry partially, thus presenting us with an interesting opportunity to make non-trivial tests of the AdS / CFT duality.