D-geometric structure of orbifolds

We study D-branes on abelian orbifolds C/ZN for d = 2, 3. The toric data describing the D-brane vacuum moduli space, which represents the geometry probed by D-branes, has certain redundancy compared with the classical geometric description of the orbifolds. We show that the redundancy has a simple combinatorial structure and find analytic expressions for degrees of the redundancy. For d = 2 the structure of the redundancy has a connection with representations of SU(N) Lie algebra, which provides a new correspondence between geometry and representation theory. We also prove that non-geometric phases do not appear in the Kähler moduli space for d = 2. ∗e-mail address:[email protected] 1