  We use holography to study (3+1)-dimensional N=4 supersymmetric SU(Nc)
Yang-Mills theory (SYM) in the large-Nc and large coupling limits, with a
(2+1)-dimensional interface where the Yang-Mills coupling or theta-angle
changes value, or "jumps." We consider interfaces that either break all
supersymmetry or that preserve half of the N=4 supersymmetry thanks to certain
operators localized to the interface. Specifically, we compute the expectation
values of a straight timelike Wilson line and of a rectangular Wilson loop in
the fundamental representation of SU(Nc). The former gives us the self-energy
of a heavy test charge while the latter gives us the potential between heavy
test charges. A jumping coupling or theta-angle acts much like a dielectric
interface in electromagnetism: a self-energy or potential includes the effects
of image charges. N=4 SYM with a jumping theta-angle may also be interpreted as
the low-energy effective description of a fractional topological insulator, as
we explain in detail. For non-supersymmetric interfaces, we find that the
self-energy and potential are qualitatively similar to those in
electromagnetism, despite the differences between N=4 SYM and electromagnetism.
For supersymmetric interfaces, we find dramatic differences from
electromagnetism which depend sensitively on the coupling of the test charge to
the adjoint scalars of N=4 SYM. In particular, we find one special case where a
test charge has vanishing image charge.
