Tue, 14 Oct 2025
15:30
15:30
L4
Vafa-Witten invariants from modular anomaly
Sergey Alexandrov
(Montpelier)
Abstract
I'll present a modular anomaly equation satisfied by generating functions of refined Vafa-Witten invariants
for the gauge group $U(N)$ on complex surfaces with $b_1=0$ and $b_2^+=1$,
which has been derived from S-duality of string theory.
I'll show how this equation can used to find explicit expressions for these generating functions
(and their modular completions) on $\mathbb{CP}^2$, Hirzebruch and del Pezzo surfaces.
The construction for $\mathbb{CP}^2$ suggests also a new form of blow-up identities.