Volume of moduli space of non-Abelian BPS domain-walls is exactly obtained inU(N_c) gauge theory with N_f matters. The volume of the moduli space isformulated, without an explicit metric, by a path integral under constraints onBPS equations. The path integral over fields reduces to a finite dimensionalcontour integral by a localization mechanism. Our volume formula satisfies aSeiberg like duality between moduli spaces of the U(N_c) and U(N_f-N_c)non-Abelian BPS domain-walls in a strong coupling region. We also find aT-duality between domain-walls and vortices on a cylinder. The moduli spacevolume of non-Abelian local (N_c=N_f) vortices on the cylinder agrees exactlywith that on a sphere. The volume formula reveals various geometricalproperties of the moduli space.
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