I describe a program, in work with T. Dimofte, to associate 2d supersymmetric field theories to triangulated 4-manifolds, complementary to recent advances associating field theories to smooth 4-manifolds initiated by Gadde-Gukov-Putrov. BPS observables in the field theory capture topological invariants of the 4-manifold. In particular, this field theoretic prescription can be used to associate chiral algebras, and corresponding graded traces, to triangulated 4-manifolds with boundary. I will propose the 2d theory that should be associated to the simplest triangulated 4-manifold, the 4-simplex, and discuss how elementary field theory dualities encode 4d Pachner moves.