Perturbative Aspects of the Deconfinement Transition: Beyond the Faddeev-Popov Paradigm (Lecture Notes in Physics)

General introduction Chapter 1: Faddeev-Popov gauge fixing and the Curci-Ferrari model 1.1 Standard gauge fixing 1.2 Infrared completion of the gauge fixing 1.3 Review of results within the Curci-Ferrari model Appendix: BRST transformations under the functional integral Chapter 2: Deconfinement transition and center symmetry 2.1 The Polyakov loop 2.2 Center symmetry 2.3 Center symmetry and gauge fixing Chapter 3: Background Field Gauges: States and Symmetries 3.1 The role of the background field with regard to center symmetry 3.2 Self-consistent backgrounds 3.3 Other symmetries 3.4 Additional remarks Chapter 4: Background Field Gauges: Weyl chambers 4.1 Constant temporal backgrounds 4.2 Winding and Weyl transformations 4.3 Weyl chambers and symmetries Appendix: Euclidean space-time symmetries Chapter 5: Yang-Mills deconfinement transition from the Curci-Ferrari model at leading order 5.1 Landau-deWitt gauge 5.2 Background field effective potential 5.3 SU(2) and SU(3) gauge groups 5.4 Thermodynamics Chapter 6: Yang-Mills deconfinement transition from the Curci-Ferrari model at next-to-leading order 6.1 Feynman rules and color conservation 6.2 Two-loop effective potential 6.3 Next-to-leading order Polyakov loop 6.4 Results Chapter 7: More on the relation between the center symmetry group and the deconfinement transition 7.1 Polyakov loops in other representations 7.2 SU(4) Weyl chambers 7.3 One-loop results 7.4 Casimir scaling Chapter 8: Background field gauges: adding quarks and density 8.1 General considerations 8.2 Continuum sign problems 8.3 Background field gauges Chapter 9: QCD decofinement transition in the heavy quark regime 9.1 Background effective potential 9.2 Phase structure at vanishing chemical potential 9.3 Phase structure at imaginary chemical potential 9.4 Phase structure at real chemical potential Chapter 10: A novel look at background field methods at finite temperature 10.1 Limitations of the standard approach 10.2 Center-symmetric Landau gauge 10.3 Implementation within the Curci-Ferrari model 10.4 Results 10.5 Connection to the self-consistent backgrounds Conclusions and outlook Appendix A: The SU(N) Lie algebra Appendix B: Evaluating Matsubara sums