### Abstract

We consider the free energy W[J] = Wk(H) of QCD coupled to an external source J_{μ}^{b}(x) = H_{μ}^{b}cos(k-x), where H_{μ}^{b} 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 W_{k}(H) and an exact asymptotic expression for W_{k}(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 ∂W_{k}(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 W_{k}(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) |
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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

- General

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## Cite this

*Proceedings of Science*.