Fivebranes and resolved deformed G₂ manifolds

We study supergravity solutions corresponding to fivebranes wrapped on a three-sphere inside a G_2 holonomy manifold. By changing a parameter the solutions interpolate between a G_2 manifold X_i \cong S^3 x R^4 with flux on a three-sphere and a distinct G_2 manifold X_j \cong S^3 x R^4 with branes on another three-sphere. Therefore, these realise a G_2 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 G_2 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 G_2 manifold S^3 x R^4.