Fractional Branes in Non-compact Type IIA Orientifolds

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We study fractional D-branes in the Type-IIA theory on a non-compact orientifold of the orbifold C³/Z₃ in the boundary state formalism. We find that the fractional D0-branes of the orbifold theory become unstable due to the presence of a tachyon, while there is a stable D-instanton whose tachyon gets projected out. We propose that the D-instanton is obtained after tachyon condensation. We evidence this by calculating the Whitehead group of the Abelian category of objects corresponding to the boundary states as being isomorphic to Z₂.