Advances in perturbative thermal field theory

TL;DR

This work surveys perturbative thermal field theory across scalars, gauge theories, and gravity, emphasizing how effective field theories and hard-thermal/dense-loop resummations restore predictive power at high temperature and density. It details imaginary-time and real-time formalisms, the emergence of thermal masses, dimensional reduction, and HTL/HDL frameworks, and discusses next-to-leading order corrections and resummations beyond HTL. The review highlights both successes (e.g., improved convergence and lattice agreement in QCD thermodynamics) and fundamental limits (magnetostatic nonperturbative effects, ultrasoft physics), while outlining implications for heavy-ion physics and early-universe cosmology. Overall, it argues that a quasiparticle picture with carefully organized resummations provides quantitative insight into hot QCD, though nonperturbative sectors remain essential for a complete description.

Abstract

The progress of the last decade in perturbative quantum field theory at high temperature and density made possible by the use of effective field theories and hard-thermal/dense-loop resummations in ultrarelativistic gauge theories is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far are given together with references to a few most recent developments and open problems.

Figures (18)

• Figure 1: Complex time path in the Schwinger-Keldysh real-time formalism
• Figure 2: Ring and extended ring or "foam" diagrams
• Figure 3: One-loop correction to the self-energy in scalar $\phi^4$ theory, and some-higher-loop diagrams with increasing degree of infrared singularity when the propagators are massless
• Figure 4: Thermal mass in large-$N$$\phi^4$-theory as a function of $g(\bar{\mu}=2\pi T)$ together with the perturbative results msc accurate to order $g^2$, $g^3$, …, $g^{10}$. The $g^3$ result is the one reaching zero at $g\approx 1$; its Padé-improved version mthscPade is given by the long-dashed line. The short-dashed line just below the exact result is obtained by solving the quadratic gap equation mtruncgap, which is also perturbatively equivalent to the order $g^3$ result.
• Figure 5: Strictly perturbative results for the thermal pressure of pure glue QCD normalized to the ideal-gas value as a function of $\alpha_s(\bar{\mu}=2\pi T)$.