(0,2) Dualities and the 4-Simplex

Understand

We propose that a simple, Lagrangian 2d $\mathcal{N}=(0, 2)$ duality interface between the 3d $\mathcal{N}=2$ XYZ model and 3d $\mathcal{N}=2$ SQED can be associated to the simplest triangulated 4-manifold: the 4-simplex.

• We then begin to flesh out a dictionary between more general triangulated 4-manifolds with boundary and 2d $\mathcal{N}=(0, 2)$ interfaces.
• In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3,3), (2,4), and (4,2) Pachner moves.
• We check these dualities using supersymmetric half-indices.