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Full backreacted local solution for D6-branes on AdS4 × S3 × S3

Develop the fully backreacted local ten-dimensional supergravity solution for the compact AdS4 × S3 × S3 nearly-Kähler compactification of type IIA with wrapped D6-branes, going beyond the smeared approximation and completing the construction on the compact space.

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Background

Nearly-Kähler compactifications of type IIA on S3 × S3 with D6-branes have been discussed in the literature, and smeared treatments exist. However, a complete local backreaction on the compact space has not been provided.

A full local solution would illuminate the precise M-theory uplift to weak G2-holonomy manifolds and contribute to the broader program of controlled, supersymmetric Freund–Rubin vacua without smearing.

References

Although ref. alluded to a local treatment of the D6-branes by considering the flat space limit close to the branes, the details of the full backreacted solution on the compact space $S3\times S3$ have not been worked out yet.

— Weak $G_2$-manifolds and scale separation in M-theory from type IIA backgrounds (2408.16609 - Hemelryck, 29 Aug 2024) in Section 3, Weak G2 holonomy and M-theory compactifications