An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on ${\mathbb{P}}^2$

Kathrin Bringmann, Caner Nazaroglu

Topologically twisted $\mathcal{N}=4$ super Yang-Mills theory has a partition function that counts Euler numbers of instanton moduli spaces. On the manifold ${\mathbb{P}}^2$ and wi…