Uniqueness of infrared asymptotics in Landau gauge Yang-Mills theory

We uniquely determine the infrared asymptotics of Green functions in Landau gauge Yang-Mills theory. They have to satisfy both the Dyson-Schwinger equations and functional renormalization group equations. Then, the requirement of consistency fixes the relation between the infrared power laws of these Green functions. We discuss consequences for the interpretation of recent results from lattice QCD.

Figure 1

Functional DSE for the effective action. Filled circles denote fully dressed field-dependent propagators (12). Empty circles denote fully dressed field-dependent vertices, and dots denote field-dependent bare vertices.

Figure 2

Functional flow for the effective action. Filled circles denote fully dressed field-dependent propagators (12). Crosses denote the regulator insertion ${\partial }_{t}R$.

Figure 3

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

Figure 4

Dyson-Schwinger equation for the ghost-gluon vertex, derived via Eq. (10). All internal propagators are taken to be fully dressed. The ellipsis denotes two-loop diagrams, which are not needed for our analysis.

Figure 5

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.

Figure 6

Functional renormalization group equations for the ghost-gluon vertex. All propagators and vertices are fully dressed. Only one possible insertion of the infrared cutoff function per diagram is shown.

Figure 7

Functional renormalization group equations for the three-gluon vertex. All internal propagators are taken to be fully dressed. Only one possible insertion of the infrared cutoff function per diagram is shown.

Figure 8

Functional renormalization group equations for the four-gluon vertex. All internal propagators are taken to be fully dressed. Only one possible insertion of the infrared cutoff function per diagram is shown.