Level-rank duality of untwisted and twisted D-branes of the soˆ(N)K WZW model

We analyze the level-rank duality of untwisted and ε-twisted D-branes of the soˆ(N)K WZW model. Untwisted D-branes of soˆ(N)K are characterized by integrable tensor and spinor representations of soˆ(N)K. Level-rank duality maps untwisted soˆ(N)K D-branes corresponding to (equivalence classes of ) tensor representations onto those of soˆ(K)N. The ε-twisted D-branes of soˆ(2n)2k are characterized by (a subset of ) integrable tensor and spinor representations of soˆ(2n−1)2k+1. Level-rank duality maps spinor ε-twisted soˆ(2n)2k D-branes onto those of soˆ(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.