The Partition Function Of Argyres-Douglas Theory On A Four-Manifold

Using the $u$-plane integral as a tool, we derive a formula for the partition function of the simplest nontrivial (topologically twisted) Argyres-Douglas theory on compact, oriented, simply connected, four-manifolds without boundary and with $b_2^{+}>0$. The result can be expressed in terms of classical cohomological invariants and Seiberg-Witten invariants. Our results hint at the existence of standard four-manifolds that are not of Seiberg-Witten simple type.