We analyze the level-rank duality of untwisted and ε-twisted D-branes of the so(N ) K WZW model. Untwisted D-branes of so(N ) K are characterized by integrable tensor and spinor representations of so(N ) K . Level-rank duality maps untwisted so(N ) K D-branes corresponding to (equivalence classes of) tensor representations onto those of so(K) N . The ε-twisted D-branes of so(2n) 2k are characterized by (a subset of) integrable tensor and spinor representations of so(2n − 1) 2k+1 . Level-rank duality maps spinor ε-twisted so(2n) 2k D-branes onto those of so(2k) 2n . For both untwisted and ε-twisted D-branes, we prove that the spectrum of an open string ending on these D-branes is isomorphic to the spectrum of an open string ending on the level-rank-dual D-branes.

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