The infrared behavior of Landau gauge Yang-Mills theory in d=2, 3 and 4 dimensions

TL;DR

This paper develops a power counting scheme for the infrared behavior of Landau gauge Yang-Mills theory across dimensions, revealing qualitative similarities and weak dependence on IR exponents, with implications for lattice simulations.

Contribution

It introduces a dimension-independent power counting framework for infrared analysis of Yang-Mills theory, showing consistent qualitative behavior across 2, 3, and 4 dimensions.

Findings

Infrared exponents are similar across dimensions.

Loop integrals depend weakly on IR exponents.

Lattice simulations can provide qualitative insights.

Abstract

We develop a general power counting scheme for the infrared limit of Landau gauge SU(N) Yang-Mills theory in arbitrary dimensions. Employing a skeleton expansion, we find that the infrared behavior is qualitatively independent of the spacetime dimension d. In the cases d=2, 3 and 4 even the quantitative results for the infrared exponents of the vertices differ only slightly. Therefore, corresponding lattice simulations provide interesting qualitative information for the physical case. We furthermore find that the loop integrals depend only weakly on the numerical values of the IR exponents.