A new fractional D2-brane, G2 holonomy and T-duality

Recently, a new example of a complete non-compact Ricci-flat metric of G2 holonomy was constructed, which has an asymptotically locally conical structure at infinity with a circular direction whose radius stabilizes. 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 stabilized circle, we obtain the type IIB description of the fractional brane, which now corresponds to a D3-brane with one of its worldvolume directions wrapped around the circle.

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