Abstract
We give an analytic demonstration that the -dimensional large pure Yang-Mills theory, compactified on a small so that the coupling constant at the compactification scale is very small, has a first order deconfinement transition as a function of temperature. We do this by explicitly computing the relevant terms in the canonical partition function up to three-loop order; this is necessary because the leading (one-loop) result for the phase transition is precisely on the border line between a first order and a second order transition. Since numerical work strongly suggests that the infinite-volume large theory also has a first order deconfinement transition, we conjecture that the phase structure is independent of the size of the . To deal with divergences in our calculations, we are led to introduce a novel method of regularization useful for non-Abelian gauge theory on .
- Received 7 April 2005
DOI:https://doi.org/10.1103/PhysRevD.71.125018
©2005 American Physical Society