文章基本信息

标题：Exact bounds on the free energy in QCD
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作者：D. Zwanziger
期刊名称：PoS - Proceedings of Science
印刷版ISSN：1824-8039
出版年度：2011
卷号：2011
期号：QCD-TNT-ll
出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jbm (x) = Hb m cos(k x), where Hb m is, by analogy with spin models, an external “magnetic” field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volumeWk(H)=V and the average magnetization m(k;H) = 1 V ¶Wk(H) ¶H vanish in the limit of constant external field k!0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) 6= 0, at k = 0. This would imply a non-analyticity in Wk(H) at k = 0. We also give some general properties of the free energy W(J) for arbitrary J(x). Finally we present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.