Disk, interval, point: on constructions of quantum field theories with holomorphic action functionals

Bosonic quantum field theories with holomorphic action functionals are realized by two types of constructions involving supersymmetric quantum field theories, compactified on an interval in one type and compactified on a disk and deformed in the other. We establish the equivalence between the two types of constructions by reducing the disk to the interval and the interval to a point. As examples, we discuss constructions of zero-dimensional gauged sigma model, gauged quantum mechanics, gauged symplectic bosons in two dimensions, and Chern-Simons theory and its higher-dimensional variants.