Exploratory study of the temperature dependence of magnetic vertices in SU(2) Landau gauge Yang--Mills theory

TL;DR

This study investigates how the three-point functions in SU(2) Landau gauge Yang-Mills theory change with temperature, revealing that the three-gluon vertex is sensitive to the phase transition, unlike the ghost-gluon vertex.

Contribution

First lattice analysis of the thermal behavior of three-point functions in SU(2) Landau gauge Yang-Mills theory, highlighting the differential impact of phase transition on these vertices.

Findings

Three-gluon vertex is significantly affected by the phase transition.

Ghost-gluon vertex remains relatively unchanged across the transition.

Thermal effects are more pronounced in the chromomagnetic sector.

Abstract

Vertices describe the interactions between the fundamental degrees of freedom, and are therefore of vital importance in many ab-initio descriptions of field theory, especially using functional methods. To this end, we present the first lattice study of the thermal behavior of (minimal) Landau-gauge SU(2) Yang--Mills three-point functions, i.e. three-gluon and ghost-gluon vertices. Focusing on the chromomagnetic sector, we find that the phase transition mainly affects the three-gluon vertex, while the ghost-gluon vertex is relatively inert.