Nahm's equations, $N=1^{*}$ domain walls, and D-strings in $AdS_{5} \times S_{5}$

Abstract

We consider the following two problems: classical domain walls in the ${\\cal N} =1^*$ 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 may correspond to heavy monopoles in higher representations of a non Abelian gauge group.