  Motivated by the question of exploring the "theory space" of quantum field
theories, we review the concept of "decomposing" and "gluing" quantum field
theories. We explain this in the context of three-dimensional $\mathcal{N}=2$
supersymmetric domain walls inside four-dimensional $\mathcal{N}=2$ theories,
where the latter arise from the 6d $(2,0)$ theory compactified on Riemann
surfaces. We find that $S^3$ partition functions of the three-dimensional
theories can be interpreted as partition functions of a three-dimensional
topological quantum field theory.
