Fivebranes and resolved deformed G₂ manifolds

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We study supergravity solutions corresponding to fivebranes wrapped on a three-sphere inside a G₂ holonomy manifold. By changing a parameter the solutions interpolate between a G₂ manifold Xᵢ S³ x R⁴ with flux on a three-sphere and a distinct G₂ manifold Xⱼ S³ x R⁴ with branes on another three-sphere. Therefore, these realise a G₂ geometric transition purely in the supergravity context. We can add D2 brane charge by applying a simple transformation to the initial solution and we obtain one-parameter deformations of warped G₂ holonomy backgrounds. These solutions suggest a connection between the N=1 Chern-Simons theory on the fivebranes and the field theory dual to D2 branes and fractional NS5 branes, transverse to the G₂ manifold S³ x R⁴.