  We study 4D systems in which parameters of the theory have position
dependence in one spatial direction. In the limit where these parameters jump,
this can lead to 3D interfaces supporting localized degrees of freedom. A
priori, this sort of position dependence can occur at either weak or strong
coupling. Demanding time-reversal invariance for $U(1)$ gauge theories with a
duality group $\Gamma \subset SL(2,\mathbb{Z})$ leads to interfaces at strong
coupling which are characterized by the real component of a modular curve
specified by $\Gamma$. This provides a geometric method for extracting the
electric and magnetic charges of possible localized states. We illustrate these
general considerations by analyzing some 4D $\mathcal{N} = 2$ theories with 3D
interfaces. These 4D systems can also be interpreted as descending from a
six-dimensional theory compactified on a three-manifold generated by a family
of Riemann surfaces fibered over the real line. We show more generally that 6D
superconformal field theories compactified on such spaces also produce trapped
matter by using the known structure of anomalies in the resulting 4D bulk
theories.
