O(D) invariant tachyon condensates in the 1/D expansion

We consider the problem of condensation of open string tachyon fields which have an O(D) symmetric profile. This problem is described by a boundary conformal field theory with D scalar fields perturbed by relevant boundary operators with O(D) symmetry. The model is exactly solvable in the large D limit and we analyze its 1/D expansion. We find that this expansion is only consistent for tachyon fields which are polynomials. In that case, we show that the theory is renormalized by normal ordering the interaction. We derive an expression for the tachyon potential which reproduces the exact potential for the quadratic tachyon profile. It can be used to correct the action which has been derived in that case iteratively in derivatives of the tachyon field.