A New Fractional D2-brane, G_2 Holonomy and T-duality

TL;DR

This paper constructs a new G_2 holonomy metric, finds a harmonic 3-form, and uses T-duality to relate fractional D2-branes to D3-branes in type IIB string theory.

Contribution

It introduces a novel G_2 holonomy metric with a stabilized circle and explicitly constructs a fractional D2-brane solution using harmonic forms.

Findings

Explicit G_2 holonomy metric with asymptotically locally conical structure

Construction of a regular harmonic 3-form in the new metric

T-duality relates fractional D2-branes to D3-branes in type IIB

Abstract

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.