Sumati Surya (Raman Research Institute, Bangalore, India)
Marco Usula (KU Leuven, Université Libre de Bruxelles)
The Nahm pole boundary condition was introduced by Mazzeo and Witten in order to study an elliptic boundary problem for solutions of the Kapustin--WItten equation, a complex version of the classical instanton equation. In this talk, I will discuss the Nahm pole condition for self-dual instantons on a compact manifold with boundary. Unlike for instantons on closed manifolds, or solutions of the KW equations with a Nahm pole, the moduli space of instantons with "fixed Nahm pole" is not a finite-dimensional object. I will present an additional asymptotic boundary condition on the connection, that guarantees that the corresponding boundary value problem is well posed (i.e. Fredholm) modulo gauge.