Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory. II.

We present a shortened and simplified version of our proof [C. S. Fischer and J. M. Pawlowski, Phys. Rev. D 75, 025012 (2007).] of the uniqueness of the scaling solution for the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. The simplification relates to a new renormalization group–invariant arrangement of Green functions applicable to general theories. As before the proof relies on the necessary consistency between Dyson-Schwinger equations and functional renormalization group equations. We also demonstrate the existence of a specific scaling solution for both, Dyson-Schwinger equations and functional renormalization group equations, that displays uniform and soft kinematic singularities.

Figure 1

Infrared asymptotics of the FRG. Filled circles denote fully dressed field dependent propagators. Empty circles denote fully dressed field dependent vertices.

Figure 2

Functional Dyson-Schwinger equation for the effective action. Filled circles denote fully dressed field dependent propagators. Empty circles denote fully dressed field dependent vertices; dots denote field dependent bare vertices.

Figure 3

Functional renormalization group equations for the gluon and ghost propagator. Filled circles denote dressed propagators, and empty circles denote dressed vertex functions. Crosses indicate insertions of the infrared cutoff function. Only one possible insertion of the infrared cutoff function per diagram is shown.

Figure 4

Dyson-Schwinger equations for the gluon and ghost propagator. Filled circles denote dressed propagators, and empty circles denote dressed vertex functions.

Figure 5

Dyson-Schwinger equations for the ghost-gluon vertex. Empty circles denote dressed vertex functions. All internal propagators are dressed; the corresponding filled circles have been omitted for clarity of the figures. One-loop diagrams with the same scaling behavior are only shown once. The ellipses denotes the other one- and two-loop diagrams which are not needed for our analysis.

Figure 6

General Dyson-Schwinger equations for ${\Gamma }^{(2n,m)}$. The straight legs denote either ghost or gluon lines with multiplicity given below the diagram, respectively.

Figure 7

Infrared leading diagram in the DSE for the ghost-gluon vertex.

Figure 8

Functional renormalization group equation for the effective action. Filled circles denote fully dressed field dependent propagators. Crosses denote the regulator insertion ${\partial }_{t}R$.

Figure 9

Diagram classes with kinematical scaling of only part of the vertices.

Figure 10

Example from an exceptional class of diagrams with kinematical scaling of only part of the vertices.