Holographic Wilson loops, dielectric interfaces, and topological insulators

We use holography to study (3 _ 1)-dimensional N = 4 supersymmetric SU(N-c)Yang-Mills theory (SYM) in the large-N-c 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(N-c). 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: the 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 nonsupersymmetric 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 a vanishing image charge.