$\mathrm{SU}(r)$ Vafa-Witten invariants, Ramanujan's continued fractions, and cosmic strings

L. Göttsche, M. Kool, T. Laarakker

We conjecture a structure formula for the $\mathrm{SU}(r)$ Vafa-Witten partition function for surfaces with holomorphic 2-form. The conjecture is based on $S$-duality and a structu…