Nahm Equations and Boundary Conditions

TL;DR

This work derives boundary conditions for Nahm's equations from a type IIB brane setup with $N$ D1-branes perpendicular to a D3-brane. By requiring a supersymmetric vacuum on the D1-brane world-volume, the problem reduces to Nahm's equations with a delta-function source at $s=0$, provided by hypermultiplets from the 1-3 sector (Eq. (8)). The discontinuities in the Nahm data thus have a brane-origin interpretation and connect the monopole moduli problem to localized impurity-like matter. The paper discusses potential stringy regularization of the induced singularities and notes connections to Kapustin–Sethi, with possible extensions to M-theory for a deeper understanding of the boundary conditions.

Abstract

We derive certain boundary conditions in Nahm's equations by considering a system of N parallel D1-branes perpendicular to a D3-brane in type IIB string theory.