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The finite volume problem of O(2N) sigma models with integrable diagonalboundaries on a finite interval is investigated. The double row transfer matrixis diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equationsfor the particle rapidities and the accompanying Bethe Ansatz equations arederived.

Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries