Nahm's equations, $N=1^{\ast }$ domain walls, and D-strings in $Ad{S}_{5}x{S}_5$

Abstract

We consider the following two problems: classical domain walls in the $N=1^{\ast }$ 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.

Latex, 26 pages, 3 figures, uses JHEP.cls; v4: discussion of holographic interpretation of `fuzzy D-string' configurations modified. Minor esthetic changes otherwise

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