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Incidental brane defects

In the models of brane construction, the isometry of a compactified space might be broken by branes. In four-dimensional effective Lagrangian, the breaking of the isometry is seen as the spontaneous breaking of the corresponding effective symmetry. Then it seems natural to expect that there are various kinds of defects that will be implemented by the spontaneous symmetry breaking. These defects are parametrized by the brane positions. In this paper we consider two kinds of such ``brane defects'', which are formed by the local fluctuations of the locations of branes along their transversal directions. The fluctuation of a brane position might leads to winding (or wraping) around a non-contractible circle of the compactified space. These ``primary'' brane defects are already discussed by several authors. On the other hand, if there are multiple branes in the compactified space and their configuration in a compactified space is determined by the potential that depends only on their relative positions, one might find incidental symmetry in the effective potential, which is spontaneously broken by branes. We examined the latter ``incidental'' symmetry breakings a