Path integral derivations of K-theoretic Donaldson invariants

We discuss topologically twisted five-dimensional SU(2) supersymmetric Yang-Mills theory on M4 x S1, where M4 is a smooth closed four-manifold. We provide two different path integral derivations of certain correlation functions, which can be identified with the K-theoretic version of the Donaldson invariants. In particular we derive their wall-crossing formula, first in the so-called U-plane integral approach and in the perspective of instanton counting. The result reproduces and generalizes the work of Gottsche, Nakajima, and Yoshioka in 2006.