  We build the framework for performing loop computations in the defect version
of N=4 super Yang-Mills theory which is dual to the probe D5-D3 brane system
with background gauge-field flux. In this dCFT, a codimension-one defect
separates two regions of space-time with different ranks of the gauge group and
three of the scalar fields acquire non-vanishing and space-time-dependent
vacuum expectation values. The latter leads to a highly non-trivial mass mixing
problem between different colour and flavour components, which we solve using
fuzzy-sphere coordinates. Furthermore, the resulting space-time dependence of
the theory's Minkowski space propagators is handled by reformulating these as
propagators in an effective AdS4. Subsequently, we initiate the computation of
quantum corrections. The one-loop correction to the one-point function of any
local gauge-invariant scalar operator is shown to receive contributions from
only two Feynman diagrams. We regulate these diagrams using dimensional
reduction, finding that one of the two diagrams vanishes, and discuss the
procedure for calculating the one-point function of a generic operator from the
SU(2) subsector. Finally, we explicitly evaluate the one-loop correction to the
one-point function of the BPS vacuum state, finding perfect agreement with an
earlier string-theory prediction. This constitutes a highly non-trivial test of
the gauge-gravity duality in a situation where both supersymmetry and conformal
symmetry are partially broken.
