Geometric Approach to 3D Interfaces at Strong Coupling

Understand

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 $\Gamma$.