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

We analyze the level-rank duality of untwisted and ε-twisted D-branes of the over(so, ̂) (N)K WZW model. Untwisted D-branes of over(so, ̂) (N)K are characterized by integrable tensor and spinor representations of over(so, ̂) (N)K. Level-rank duality maps untwisted over(so, ̂) (N)K D-branes corresponding to (equivalence classes of ) tensor representations onto those of over(so, ̂) (K)N. The ε-twisted D-branes of over(so, ̂) (2 n)2 k are characterized by (a subset of ) integrable tensor and spinor representations of over(so, ̂) (2 n - 1)2 k + 1. Level-rank duality maps spinor ε-twisted over(so, ̂) (2 n)2 k D-branes onto those of over(so, ̂) (2 k)2 n. 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. © 2007 Elsevier B.V. All rights reserved.