Fractional branes on a non-compact orbifold

Abstract

Fractional branes on the non-compact orbifold C3 /Z5 are studied. First, the boundary state description of the fractional branes are obtained. The open-string Witten index calculated using these states reproduces the adjacency matrix of the quiver of Z5 . Then, using the toric crepant resolution of the orbifold C3 /Z5 and invoking the local mirror principle, B-type branes wrapped on the holomorphic cycles of the resolution are studied. The boundary states corresponding to the five fractional branes are identified as bound states of BPS D-branes wrapping the 0-, 2-and 4-cycles in the exceptional divisor of the resolution of C3 /Z5 .