The Interplay Between $θ$ and T

Details The Interplay Between $θ$ and T The Interplay Between $θ$ and T

2000-03-23

arxiv.org/abs/hep-th/0003216v1

JHEP 0006 (2000) 032

Physics

High Energy Physics

High Energy Physics - Theory

14 pages, 1 eps figure

Scientific paper

10.1088/1126-6708/2000/06/032

We extend a recent computation of the dependence of the free energy, F, on the noncommutative scale $\theta$ to theories with very different UV sensitivity. The temperature dependence of $F$ strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, $F_{\rm np}$, at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and can be traced to modes whose thermal wavelengths become smaller than the noncommutativity scale. The temperature dependence of $F_{\rm np}$ can then be calculated at high temperature using classical statistical mechanics, without encountering a UV catastrophe even in large number of dimensions. This result is a telltale sign of the low number of degrees of freedom contributing to $F$ in the non-planar sector at high temperature. Such behavior is in marked contrast to what would happen in a field theory with a random set of higher derivative interactions.

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