Level-rank duality of untwisted and twisted D-branes of the [formula omitted] WZW model

Abstract

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