Open String Gravity?

We present a new application of Boundary String Field Theory: calculating the induced-gravity action on a D-brane. Using a simple quadratic tachyon potential to model a D-brane fluctuating in the flat target space we derive the effective action in terms of the extrinsic curvature to all orders in alpha’. We identify both the Born-Infeld structure as well as the Einstein-Hilbert term at order alpha’. This corroborates the conjectured existence of the latter term in the brane-world scenarios. The higher order terms in Ricci scalar and extrinsic curvature suggest a pattern which calls for an explanation.