Nahm's equations, $N=1^*$ domain walls, and D-strings in $AdS_5 x S_5$

TL;DR

This paper links Nahm's equations to domain walls in N=1* SYM and D-strings in AdS/CFT, revealing their common mathematical structure and implications for gauge/string duality.

Contribution

It demonstrates that both domain walls and D-strings are described by Nahm's equations with novel boundary conditions, connecting different physical phenomena through a unified mathematical framework.

Findings

Nahm's equations characterize domain walls and D-strings.

Fuzzy sphere D-string configurations relate to Wilson-'t Hooft lines.

Analysis of the moduli space of solutions enhances understanding of dualities.

Abstract

We consider the following two problems: classical domain walls in the $N=1^*$ mass deformation of the maximally supersymmetric Yang Mills theory, and D-strings as external magnetic sources in the context of the AdS/CFT correspondence. We show that they are both described by Nahm's equations with unconventional boundary conditions, and analyze the relevant moduli space of solutions. We argue that general `fuzzy sphere' configurations of D-strings in AdS$_5$ correspond to Wilson-'t Hooft lines in higher representations of the dual SU(n) gauge theory.