TY - JOUR

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

AU - Maas, Axel

AU - Zwanziger, Daniel

N1 - Publisher Copyright:
© Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence.

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 Jbμ is a source for the gluon field Abμ 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 Jbμ is a source for the gluon field Abμ 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.

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U2 - 10.22323/1.193.0047

DO - 10.22323/1.193.0047

M3 - Conference article

AN - SCOPUS:84977142916

SN - 1824-8039

VL - 02-06-September-2013

JO - Proceedings of Science

JF - Proceedings of Science

M1 - 047

T2 - 3rd QCD-TNT Workshop 2013

Y2 - 2 September 2013 through 6 September 2013

ER -