### Abstract

We exhibit some general bounds on the free energy W(J) in an SU(N) gauge theory, where J^{b}_{μ} is a source for the gluon field A^{b}_{μ} in the minimal Landau gauge, and W(J) is the generating functional of connected correlators, expW(J) = (exp(J,A)). We then specialize to a source J(x) = hcos(k-x) of definite momentum k and source strength h, and study the gluon propagator D(k,h) in the presence of this source. Among other relations, we prove f^{∞}_{0} dh D(k,h) ≤ V2k, which implies lim_{k→0} D(k, h) = 0, for all positive h>0. This means that the system does not respond to a static color probe, no matter how strong. We also present numerical evaluations of the free energy W(k, h) and the gluon propagator D(k, h) for the case of SU(2) Yang-Mills theory in dimensions 2, 3 and 4 which are consistent with these findings, and we compare with recent lattice calculations at h = 0 which indicate that the gluon propagator in the minimum Landau gauge is finite, lim_{k→0} D(k, 0) > 0. These lattice data together with our analytic results imply a jump in the value of D(k, h) at h = 0 and k = 0, and the value of D(k, h) at this point depends on the order of limits.

Original language | English (US) |
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Article number | 047 |

Journal | Proceedings of Science |

Volume | 02-06-September-2013 |

State | Published - Feb 12 2014 |

Event | 3rd QCD-TNT Workshop 2013 - Villazzano, Trento, Italy Duration: Sep 2 2013 → Sep 6 2013 |

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### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*,

*02-06-September-2013*, [047].