Level-rank duality of D-branes on the SU(N) group manifold

TL;DR

This paper investigates the implications of level-rank duality on D-branes in SU(N) group manifolds, revealing charge relations and algebra isomorphisms in specific cases, advancing understanding of D-brane classifications.

Contribution

It demonstrates charge relations and algebra isomorphisms for untwisted D-branes under level-rank duality on SU(N) manifolds, specifically for odd N+K, linking twisted K-theory classifications.

Findings

Charge relations between su(N)_K and su(K)_N theories for odd N+K.

Isomorphism between charge algebras in these theories.

Enhanced understanding of D-brane classifications via level-rank duality.

Abstract

The consequences of level-rank duality for untwisted D-branes on an SU(N) group manifold are explored. Relations are found between the charges of D-branes (which are classified by twisted K-theory) belonging to su(N)_K and su(K)_N WZW theories, in the case of odd N+K. An isomorphism between the charge algebras is also demonstrated in this case.