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.
An Exact Solution of BPS Domain Wall Junction
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abstract
An exact solution of domain wall junction is obtained in a four-dimensional N=1 supersymmetric U(1) X U(1)' gauge theory with three pairs of chiral superfields which is motivated by the N=2 SU(2) gauge theory with one flavor perturbed by an adjoint scalar mass. The solution allows us to evaluate various quantities including a new central charge Y_k associated with the junction besides Z_k which appears already in domain walls. We find that the new central charge Y_k gives a negative contribution to the mass of the domain wall junction whereas the central charge Z_k gives a dominant positive contribution. One has to be cautious to identify the central charge Y_k alone as the mass of the junction.
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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.