Perturbative Thermal QCD: Formalism and Applications

Abstract

In this review article, we discuss the current status and future prospects of perturbation theory as a means of studying the equilibrium thermodynamic and near-equilibrium transport properties of deconfined QCD matter. We begin with a brief introduction to the general topic, after which we review in some detail the foundations and modern techniques of the real- and imaginary-time formalisms of thermal field theory, covering e.g. the different bases used in the real-time formalism and the resummations required to deal with soft and collinear contributions. After this, we discuss the current status of applications of these techniques, including topics such as electromagnetic rates, transport coefficients, jet quenching, heavy quarks and quarkonia, and the Equations of State of hot quark-gluon plasma as well as cold and dense quark matter. Finally, we conclude with our view of the future directions of the field, i.e. how we anticipate perturbative calculations to contribute to our collective understanding of strongly interacting matter in the coming years.

arXiv comment137 pages, 44 figures. v4: Version published in Physics Reports; two typographical errors corrected from v3

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• The shear channel spectral function in hot Yang-Mills theory
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• Three-loop HTL Free Energy for QED
• The Polyakov loop at next-to-next-to leading order
• The diagonal and off-diagonal quark number susceptibility of high temperature and finite density QCD
• IBP methods at finite temperature
• Photon Production from a Quark-Gluon-Plasma at Finite Baryon Chemical Potential
• Renormalization of the cyclic Wilson loop
• Three-loop HTLpt thermodynamics at finite temperature and chemical potential
• The rate of photon production in the quark-gluon plasma from lattice QCD
• The HTL Lagrangian at NLO: the photon case
• An estimate for the thermal photon rate from lattice QCD
• On the dispersion of fundamental particles in QCD and N=4 Super Yang-Mills theory
• Transverse momentum broadening and collinear radiation at NLO in the $\mathcal{N}=4$ SYM plasma
• Testing thermal photon and dilepton rates
• Polyakov loop correlator in perturbation theory
• A new method for taming tensor sum-integrals
• Thermalisation of Longitudinal Gluons
• Intermediate distance correlators in hot Yang-Mills theory
• Probing the spacetime evolution of heavy ion collisions with photons and dileptons
• Three-loop matching coefficients for hot QCD: Reduction and gauge independence
• Renormalization group improved pressure for cold and dense QCD
• Energetic di-leptons from the Quark Gluon Plasma
• A local Langevin equation for slow long-distance modes of hot non-Abelian gauge fields
• Global properties of rotating neutron stars with QCD equations of state
• Study of the gluon propagator in the large-N_f limit at finite temperature and chemical potential for weak and strong couplings
• A thermal neutrino interaction rate at NLO
• Soft thermal contributions to 3-loop gauge coupling
• The N_f^3 g^6 term in the pressure of hot QCD
• The Boltzmann Equation in Classical Yang-Mills Theory
• Towards generating a new supernova equation of state: A systematic analysis of cold hybrid stars
• Energy momentum tensor correlators in hot Yang-Mills theory: holography confronts lattice and perturbation theory
• Thermal width of the Higgs boson in hot QCD matter
• Finite temperature CFT results for all couplings: O(N) model in 2+1 dimensions
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• Thermal free energy of large Nf QED in 2+1 dimensions from weak to strong coupling
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• Next-to-leading order thermal photon production in a weakly-coupled plasma
• Quantum Corrections to Thermodynamic Properties in the Large $N_f$ Limit of the Quark Gluon Plasma
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