Supersymmetric Non-singular Fractional D2-branes and NS-NS 2-branes

TL;DR

This paper constructs and analyzes supersymmetric, non-singular fractional D2-brane solutions on G_2 holonomy manifolds, revealing insights into their dual 3D gauge theories and spectrum, with new Ricci-flat metrics introduced.

Contribution

It presents new regular deformed D2-brane solutions on G_2 manifolds and explores their supersymmetry and dual gauge theories, including explicit Ricci-flat metric examples.

Findings

Solutions preserve 1/16 supersymmetry.

Spectrum indicates confinement in dual theories.

Constructed new Ricci-flat metrics.

Abstract

We obtain regular deformed D2-brane solutions with fractional D2-branes arising as wrapped D4-branes. The space transverse to the D2-brane is a complete Ricci-flat 7-manifold of G_2 holonomy, which is asymptotically conical with principal orbits that are topologically CP^3 or the flag manifold SU(3)/(U(1) x U(1)). We obtain the solution by first constructing an L^2 normalisable harmonic 3-form. We also review a previously-obtained regular deformed D2-brane whose transverse space is a different 7-manifold of G_2 holonomy, with principal orbits that are topologically S^3 x S^3. This describes D2-branes with fractional NS-NS 2-branes coming from the wrapping of 5-branes, which is supported by a non-normalisable harmonic 3-form on the 7-manifold. We prove that both types of solutions are supersymmetric, preserving 1/16 of the maximal supersymmetry and hence that they are dual to {\cal N}=1 three-dimensional gauge theories. In each case, the spectrum for minimally-coupled scalars is discrete, indicating confinement in the infrared region of the dual gauge theories. We examine resolutions of other branes, and obtain necessary conditions for their regularity. The resolution of many of these seems to lie beyond supergravity. In the process of studying these questions, we construct new explicit examples of complete Ricci-flat metrics.