Dispersion relations for the self-energy in noncommutative field theories

We study the IR-UV connection in noncommutative ${\ensuremath{\varphi}}^{3}$ theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed.