String-Theory’s AdS/dCFT Duality Passes a Crucial Quantum Test

String-Theory’s AdS/dCFT Duality Passes a Crucial Quantum Test 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.