On Non-Supersymmetric CFT in Four Dimensions

We show that the $\CN=0$ theories on the self-dual D3-branes of Type 0 string theory are in the class of the previously considered tadpole-free orbifolds of $\CN = 4$ theory (although they have SO(6) global symmetry) and hence have vanishing beta function in the planar limit to all orders in 't Hooft coupling. Also, all planar amplitudes in this theory are equal to those of $\CN = 4$ theory, up to a rescaling of the coupling.