Stable sheaves with twisted sections and the Vafa-Witten equations on smooth projective surfaces (Q2017732)

This paper concerns a set of gauge-theoretic equations on smooth projective surfaces, considered by \textit{C. Vafa} and \textit{E. Witten} [Nucl. Phys., B 431, No. 1--2, 3--77 (1994; Zbl 0964.81522)] in the study of the S-duality conjecture for \(N=4\) supersymmetric Yang-Mills theory. These equations can be seen as higher-dimensional analogue of the Hitchin equations on compact Riemannian surfaces. With \(X\) a given smooth projective surface and \(E\) a holomorphic vector bundle on \(X\), the main tool is a Donaldson-type functional on the space of Hermitian metrics on \(E\).