Abstract: Equivariant localization arguments generalize the Duistermaat–Heckman formula, allowing one to express an integral on a manifold in terms of integrals over fixed point sets of a torus action. Supersymmetric localization seeks to apply these formulas to path integrals in quantum field theory. In fortuitous cases, this affords a rigorous definition of the path integral. I will explain one such example in a 2-dimensional quantum field theory built on a classical theory of maps from elliptic curves to a smooth manifold. Up to a certain choice of orientation (which may be obstructed), the path integral is well-defined. The volume of the mapping space (i.e., the path integral of 1) turns out to be the Witten genus, an invariant of smooth manifolds valued in modular forms.