Level-rank duality of untwisted and twisted D-branes

Level-rank duality of untwisted and twisted D-branes of WZW models is explored. We derive the relation between D0-brane charges of level-rank dual untwisted D-branes of suˆ(N)K and spˆ(n)k, and of level-rank dual twisted D-branes of suˆ(2n+1)2k+1. The analysis of level-rank duality of twisted D-branes of suˆ(2n+1)2k+1 is facilitated by their close relation to untwisted D-branes of spˆ(n)k. We also demonstrate level-rank duality of the spectrum of an open string stretched between untwisted or twisted D-branes in each of these cases.