We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jμb(x) = Hμbcos(k-x), where Hμb 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 volume Wk(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) ≠ 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.
|Original language||English (US)|
|Journal||Proceedings of Science|
|State||Published - 2011|
|Event||International Workshop on QCD Green's Functions, Confinement and Phenomenology, QCD-TNT 2011 - Trento, Italy|
Duration: Sep 5 2011 → Sep 9 2011
ASJC Scopus subject areas