A UV completion of scalar field theory in arbitrary even dimensions

Following a previous work (hep-th/0410248), where a scalar field theory with a modified propagator and phi^4 interaction in 4 dimensions is constructed to be UV-finite, unitary and Lorentz invariant, we discuss in this paper general phi^n theory in arbitrary even space-time dimensions. We show that the theory is still UV-finite, unitary and Lorentz invariant if the propagators are chosen to meet certain simple conditions depending on the space-time dimension but independent of n. We also comment that our model is reminiscent of string theory in the way UV divergence is avoided.