The thermal heat kernel expansion and the one-loop effective action of QCD at finite temperature

Abstract

The heat kernel expansion for field theory at finite temperature is constructed. It is based on the imaginary time formalism and applies to generic Klein-Gordon operators in flat space-time. Full gauge invariance is manifest at each order of the expansion and the Polyakov loop plays an important role at any temperature. The expansion is explicitly worked out up to operators of dimension six included. The method is then applied to compute the one loop effective action of QCD at finite temperature with massless quarks. The calculation is carried out within the background field method in the $\overline{\text{MS}}$ scheme up to dimension six operators. Further, the action of the dimensionally reduced effective theory at high temperature is also computed to the same order. Existing calculations are reproduced and new results are obtained in the quark sector for which only partial results existed up to dimension six.

arXiv comment28 pages RevTeX

References in corpus (24)

• Generic Rules for High Temperature Dimensional Reduction and Their Application to the Standard Model
• Free Energy of QCD at High Temperature
• Quark-Gluon Plasma as a Condensate of Z(3) Wilson Lines
• 3d SU(N) + adjoint Higgs theory and finite temperature QCD
• Z(N) interface tension in a hot SU(N) gauge theory
• Solution to the Perturbative Infrared Catastrophe of Hot Gauge Theories
• Index-free Heat Kernel Coefficients
• The Higher Derivative Expansion of the Effective Action by the String Inspired Method. Part II
• The Relevant Scale Parameter in the High Temperature Phase of QCD
• A New Dimensionally Reduced Effective Action for QCD at High Temperature
• Three-Loop Yang-Mills beta-Function via the Covariant Background Field Method
• Calculation of Heat-Kernel Coefficients and Usage of Computer Algebra
• Parity breaking in 2+1 dimensions and finite temperature
• Diagrams for heat kernel expansions
• Covariant derivative expansion of Yang-Mills effective action at high temperatures
• The Polyakov loop and the heat kernel expansion at finite temperature
• One-Loop QCD Corrections to the Thermal Wilson Line Model
• QCD at high density/temperature
• Gauge invariant derivative expansion of the effective action at finite temperature and density and the scalar field in 2+1 dimensions
• What Have We Learned from RHIC?
• The induced Chern-Simons term at finite temperature
• On the Wess-Zumino-Witten anomalous functional at finite temperature
• Thermal Quantum Fields in Static Electromagnetic Backgrounds
• Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Cited by in corpus (34)

• Polyakov loop in chiral quark models at finite temperature
• Susceptibilities and speed of sound from PNJL model
• Two-loop QCD gauge coupling at high temperatures
• Resummation in Hot Field Theories
• Thermodynamics of the PNJL model with nonzero baryon and isospin chemical potentials
• Quantum weights of dyons and of instantons with non-trivial holonomy
• Effective Theory of Wilson Lines and Deconfinement
• Thermodynamic Properties of Strongly Interacting Matter in a Finite Volume using the Polyakov-Nambu-Jona-Lasinio model
• Dimension two condensates and the Polyakov loop above the deconfinement phase transition
• Fuzzy Bags and Wilson Lines
• Chiral Lagrangian at finite temperature from the Polyakov-Chiral Quark Model
• Small shear viscosity in the semi quark gluon plasma
• Gauge invariant effective action for the Polyakov line in the SU(N) Yang--Mills theory at high temperatures
• Thermodynamic potential with correct asymptotics for PNJL model
• Computing the temperature dependence of effective CP violation in the standard model
• Quantum-induced interactions in the moduli space of degenerate BPS domain walls
• The Polyakov loop in various representations in the confined phase of QCD
• Covariant derivative expansion of the heat kernel
• Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions
• Soft thermal contributions to 3-loop gauge coupling
• Derivative expansion of the heat kernel at finite temperature
• The abelian confinement mechanism revisited: new aspects of the Georgi-Glashow model
• Magnetic field dependent 't Hooft determinant extended Nambu--Jona-Lasinio Model
• Derivative expansion of the heat kernel in curved space
• The method of covariant symbols in curved space-time
• The strange critical endpoint and isentropic trajectories in an Extended PNJL Model with Eight Quark Interactions
• Phase diagram for strongly interacting matter in the presence of a magnetic field using the Polyakov-Nambu-Jona-Lasinio model with magnetic field dependent coupling strengths
• Two-color QCD via dimensional reduction
• Heat kernel of non-minimal gauge field kinetic operators on Moyal plane
• Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions
• One-loop effective action of QCD at high temperature using the heat kernel method
• Scattering approach for calculating one-loop effective action and vacuum energy
• Polyakov loop at low and high temperatures
• The Polyakov loop dependence of bulk viscosity of QCD matter