Reggeon field theory in zero transverse dimensions

We study Reggeon field theory in zero transverse dimensions. We calculate the renormalization-group functions in closed form and show that there is an infrared-stable fixed point. We also calculate the critical indices exactly. We find that perturbation theory cannot be used directly to calculate the renormalization-group functions in the neighborhood of the fixed point, but that Pad\'e and Borel-Pad\'e approximants can. We prove that the only singularities of the partial-wave amplitude in the angular momentum plane are isolated poles. The intercept of the leading pole approaches unity only in the limit that the bare intercept goes to infinity.