Hard Non-commutative Loops Resummation

Abstract

The non-commutative version of the euclidean $g^2\phi^4$ theory is considered. By using Wilsonian flow equations the ultraviolet renormalizability can be proved to all orders in perturbation theory. On the other hand, the infrared sector cannot be treated perturbatively and requires a resummation of the leading divergencies in the two-point function. This is analogous to what is done in the Hard Thermal Loops resummation of finite temperature field theory. Next-to-leading order corrections to the self-energy are computed, resulting in $O(g^3)$ contributions in the massless case, and $O(g^6\log g^2)$ in the massive one.Comment: 4 pages, 3 figures. The resummation procedure is now discussed also at finite ultraviolet cut-off. Minor changes in abstract and references. Final version to be published in Physical Review Letter