[Paper Review] The High-Temperature Phase of Yang-Mills Theory in Landau Gauge

Axel Maas|ArXiv.org|Jan 17, 2005

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This thesis investigates the high-temperature phase of 4D Yang-Mills theory in Landau gauge using Dyson-Schwinger equations with a novel truncation scheme. It finds that the infinite-temperature limit reduces the theory to 3D Yang-Mills coupled to a massive adjoint Higgs, and confinement persists in the transverse gluon sector, indicating a non-trivial, strongly interacting high-temperature phase with good agreement to lattice results and evidence for a first-order phase transition.

ABSTRACT

The high-temperature phase of Yang-Mills theory in Landau gauge is studied using Dyson-Schwinger equations. The propagators of the gluon and the Faddeev-Popov ghosts are obtained at finite and infinite temperature, partially analytically. The results are in good agreement with lattice results. It is found that the infrared properties are only quantitatively affected by temperature. The confinement of at least soft gluons transverse to the heat bath is established, in accordance with the Kugo-Ojima and Gribov-Zwanziger confinement scenarios. This is confirmed by investigating the corresponding Schwinger functions. The hard modes are nearly inert even at temperatures of the order of the phase transition temperature. In addition, the thermodynamic potential is analyzed and solutions for 3d-Yang-Mills theory are obtained. It is conjectured that Yang-Mills theory likely undergoes a first order phase transition, which changes a strongly interacting system into another. The phases differ mainly by the properties of the chromoelectric sector.

Motivation & Objective

• To understand the infrared and thermal properties of Yang-Mills theory at high temperatures, particularly the fate of confinement.
• To investigate whether the high-temperature phase remains strongly interacting and non-trivial, despite the expected deconfinement at the phase transition.
• To validate the Dyson-Schwinger equation approach with a new truncation scheme against lattice calculations and perturbative expectations.
• To determine the analytic structure of gluon and ghost propagators and their implications for confinement scenarios at finite temperature.
• To study thermodynamic quantities such as the thermodynamic potential and pressure, and infer the nature of the phase transition.

Proposed method

• The study employs Dyson-Schwinger equations (DSEs) for gluon, ghost, and Higgs propagators in Landau gauge at finite temperature.
• A truncation scheme is applied, focusing on ghost-loop contributions and including hard thermal loops in the infinite-temperature limit.
• The infinite-temperature limit reduces the 4D theory to a 3D Yang-Mills theory coupled to a massive adjoint Higgs field, enabling analytical and numerical solutions.
• Infrared behavior is analytically derived using asymptotic analysis, while full-momentum solutions are obtained numerically via Chebyshev expansion and global Newton methods.
• Renormalization is implemented iteratively to handle spurious divergences from Matsubara sums, ensuring stability in numerical solutions.
• The method is validated by showing convergence to the correct N→∞ limit of Matsubara frequencies and consistency with perturbative resummation at leading order.

Experimental results

Research questions

• RQ1 Does confinement persist in the high-temperature phase of Yang-Mills theory, particularly for gluons transverse to the heat bath?
• RQ2 How do the infrared properties of gluon and ghost propagators evolve as temperature increases toward the critical point?
• RQ3 To what extent does the infinite-temperature limit accurately describe the finite-temperature behavior near the phase transition?
• RQ4 What is the analytic structure of the gluon propagator, and does it support the Kugo-Ojima or Zwanziger-Gribov confinement scenarios at high temperature?
• RQ5 Is the thermodynamic potential dominated by hard or soft modes, and what does this imply about the nature of the phase transition?

Key findings

• The infinite-temperature limit yields a 3D Yang-Mills theory with a massive adjoint Higgs, and the Yang-Mills sector exhibits confinement in the infrared, indicating a non-trivial high-temperature phase.
• Numerical solutions for all propagators—gluon, ghost, and Higgs—are obtained across all momenta, showing good agreement with lattice simulations.
• The infrared properties are only quantitatively affected by finite temperature, and gluon confinement transverse to the heat bath is preserved down to the phase transition regime.
• Hard modes remain nearly inert even near the critical temperature, validating the infinite-temperature limit as a good approximation at T ≳ 3T_c.
• The Schwinger functions and analytic structure of the gluon propagator confirm that longitudinal gluons are also affected by non-perturbative effects, supporting the Kugo-Ojima and Zwanziger-Gribov confinement scenarios.
• The thermodynamic potential exhibits approximate Stefan-Boltzmann behavior, with hard modes dominating the potential, and the system likely undergoes a first-order phase transition, transitioning from a strongly interacting to another strongly interacting phase.