The interplay between θ and T

We extend a recent computation of the dependence of the free energy, F, onthe noncommutative scale $\theta$ to theories with very different UVsensitivity. The temperature dependence of $F$ strongly suggests that a reducednumber of degrees of freedom contributes to the free energy in the non-planarsector, $F_{\rm np}$, at high temperature. This phenomenon seems generic,independent of the UV sensitivity, and can be traced to modes whose thermalwavelengths become smaller than the noncommutativity scale. The temperaturedependence of $F_{\rm np}$ can then be calculated at high temperature usingclassical statistical mechanics, without encountering a UV catastrophe even inlarge number of dimensions. This result is a telltale sign of the low number ofdegrees of freedom contributing to $F$ in the non-planar sector at hightemperature. Such behavior is in marked contrast to what would happen in afield theory with a random set of higher derivative interactions.Comment: 14 pages, 1 eps figur