  Via a challenging field-theory computation, we confirm a supergravity
prediction for the non-supersymmetric D3-D7 probe-brane system with probe
geometry AdS_4 x S^2 x S^2, stabilized by fluxes. Supergravity predicts, in a
certain double-scaling limit, the value of the one-point functions of chiral
primaries of the dual defect version of N=4 SYM theory, where the fluxes
translate into SO(3) x SO(3)-symmetric, Lie-algebra-valued vacuum expectation
values for all six scalar fields. Using a generalization of the technique based
on fuzzy spherical harmonics developed for the related D3-D5 probe-brane
system, we diagonalize the resulting mass matrix of the field theory.
Subsequently, we calculate the planar one-loop correction to the vacuum
expectation values of the scalars in dimensional reduction and find that it is
UV finite and non-vanishing. We then proceed to calculating the one-loop
correction to the planar one-point function of any single-trace scalar operator
and explicitly evaluate this correction for a 1/2-BPS operator of length L at
two leading orders in the double-scaling limit, finding exact agreement with
the supergravity prediction.
