  We show that the Gukov-Witten monodromy defects of supersymmetric Yang-Mills
theory can be realized in perturbative string theory by considering an orbifold
background of the Kanno-Tachikawa type and placing stacks of fractional
D3-branes whose world-volume partially extends along the orbifold directions.
In particular, we show that turning on a constant background value for some
scalar fields in the closed string twisted sectors induces a non-trivial
profile for the gauge field and one of the complex scalars of the world-volume
theory, and that this profile exactly matches the singular behavior that one
expects for a Gukov-Witten surface defect in the $\mathcal{N}=4$ super
Yang-Mills theory. To keep the presentation as simple as possible, in this work
we restrict our analysis to surface defects corresponding to a $\mathbb{Z}_2$
orbifold and defer the study of the most general case to a companion paper.
