The exact fermion zero mode on any BPS monopole-string-domain wall background takes the profile f=Ω^{-h/4}, and its localization moves among monopoles, strings, domain walls, and convex polyhedral vacuum regions with a fermion mass shift.
Webs of Walls
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abstract
Webs of domain walls are constructed as 1/4 BPS states in d=4, N=2 supersymmetric U(Nc) gauge theories with Nf hypermultiplets in the fundamental representation. Web of walls can contain any numbers of external legs and loops like (p,q) string/5-brane webs. We find the moduli space M of a 1/4 BPS equation for wall webs to be the complex Grassmann manifold. When moduli spaces of 1/2 BPS states (parallel walls) and the vacua are removed from M, the non-compact moduli space of genuine 1/4 BPS wall webs is obtained. All the solutions are obtained explicitly and exactly in the strong gauge coupling limit. In the case of Abelian gauge theory, we work out the correspondence between configurations of wall web and the moduli space CP^{Nf-1}.
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Massless monopole-string-domain wall fermions and polyhedral vacuum fermions
The exact fermion zero mode on any BPS monopole-string-domain wall background takes the profile f=Ω^{-h/4}, and its localization moves among monopoles, strings, domain walls, and convex polyhedral vacuum regions with a fermion mass shift.