(0,2) dualities and the 4-simplex

Abstract We propose that a simple, Lagrangian 2d $$ \mathcal{N} $$ N = (0, 2) duality interface between the 3d $$ \mathcal{N} $$ N = 2 XYZ model and 3d $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = (0, 2) interfaces. In particular, we identify IR dualities of interfaces associated to local changes of 4d triangulation, governed by the (3), (2, 4), and (2, 4) Pachner moves. We check these dualities using supersymmetric half-indices. We also describe how to produce stand-alone 2d theories (as opposed to interfaces) capturing the geometry of 4-simplices and Pachner moves by making additional field-theoretic choices, and find in this context that the Pachner moves recover abelian $$ \mathcal{N} $$ N = (0, 2) trialities of Gadde-Gukov-Putrov. Our work provides new, explicit tools to explore the interplay between 2d dualities and 4-manifold geometry that has been developed in recent years.