A New Fractional D2-brane, G₂ Holonomy and T-duality

Recently, a new example of a complete non-compact Ricci-flat metric of G_2 holonomy was constructed, which has an asymptotically locally conical structure at infinity with a circular direction whose radius stabilises. In this paper we find a regular harmonic 3-form in this metric, which we then use in order to obtain an explicit solution for a fractional D2-brane configuration. By performing a T-duality transformation on the stabilised circle, we obtain the type IIB description of the fractional brane, which now corresponds to D3-brane with one of its world-volume directions wrapped around the circle.