Fractional Branes on a Non-compact Orbifold

TL;DR

This paper investigates fractional branes on a non-compact orbifold, deriving boundary states, computing the open-string Witten index, and analyzing B-branes on the resolved geometry using mirror symmetry.

Contribution

It provides a boundary state description of fractional branes on ^3/_5 and connects them to BPS D-branes on the resolved space via mirror symmetry.

Findings

Boundary states reproduce the _5 quiver adjacency matrix.

Fractional branes are identified as bound states of BPS D-branes.

The analysis links fractional branes to wrapped D-branes on the resolved geometry.

Abstract

Fractional branes on the non-compact orbifold $\C^3/\Z_5$ 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 $\Z_5$. Then, using the toric crepant resolution of the orbifold $\C^3/\Z_5$ 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 $\C^3/\Z_5$.