Description
Book SynopsisThis book offers an original view of the color confinement/deconfinement transition that occurs in non-abelian gauge theories at high temperature and/or densities. It is grounded on the fact that the standard Faddeev-Popov gauge-fixing procedure in the Landau gauge is incomplete. The proper analysis of the low energy properties of non-abelian theories in this gauge requires, therefore, the extension of the gauge-fixing procedure, beyond the Faddeev-Popov recipe.
The author reviews various applications of one such extension, based on the Curci-Ferrari model, with a special focus on the confinement/deconfinement transition, first in the case of pure Yang-Mills theory, and then, in a formal regime of Quantum Chromodynamics where all quarks are considered heavy. He shows that most qualitative aspects and also many quantitative features of the deconfinement transition can be accounted for within the model, with only one additional parameter. Moreover, these features emerge in a systematic and controlled perturbative expansion, as opposed to what would happen in a perturbative expansion within the Faddeev-Popov model.
The book is also intended as a thorough and pedagogical introduction to background field gauge techniques at finite temperature and/or density. In particular, it offers a new and promising view on the way these techniques might be applied at finite temperature. The material aims at graduate students or researchers who wish to deepen their understanding of the confinement/deconfinement transition from an analytical perspective. Basic knowledge of gauge theories at finite temperature is required, although the text is designed in a self-contained manner, with most concepts and tools introduced when needed. At the end of each chapter, a series of exercises is proposed to master the subject.
Table of ContentsGeneral 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 results7.4 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 regime9.1 Background effective potential9.2 Phase structure at vanishing chemical potential9.3 Phase structure at imaginary chemical potential9.4 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
