### 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) |
---|---|

Article number | 047 |

Journal | Unknown Journal |

Volume | 02-06-September-2013 |

State | Published - Feb 12 2014 |

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### ASJC Scopus subject areas

- General

### Cite this

*Unknown Journal*,

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

**Gluon propagator in an external field; what happens when the field is removed?** / Maas, Axel; Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Unknown Journal*, vol. 02-06-September-2013, 047.

}

TY - JOUR

T1 - Gluon propagator in an external field; what happens when the field is removed?

AU - Maas, Axel

AU - Zwanziger, Daniel

PY - 2014/2/12

Y1 - 2014/2/12

N2 - We exhibit some general bounds on the free energy W(J) in an SU(N) gauge theory, where Jb μ is a source for the gluon field Ab 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 limk→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, limk→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.

AB - We exhibit some general bounds on the free energy W(J) in an SU(N) gauge theory, where Jb μ is a source for the gluon field Ab 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 limk→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, limk→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.

UR - http://www.scopus.com/inward/record.url?scp=84977142916&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977142916&partnerID=8YFLogxK

M3 - Article

VL - 02-06-September-2013

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

M1 - 047

ER -