CiNii Books - An introduction to the confinement problem

This book addresses the confinement problem, which concerns the behavior of non-abelian gauge theories, and the force which is mediated by gauge fields, at large distances. The word "confinement" in the context of hadronic physics originally referred to the fact that quarks and gluons appear to be trapped inside mesons and baryons, from which they cannot escape. There are other, and possibly deeper meanings that can be attached to the term, and these will be explored in this book. Although the confinement problem is far from solved, much is now known about the general features of the confining force, and there are a number of very well motivated theories of confinement which are under active investigation. This volume gives a both pedagogical and concise introduction and overview of the main ideas in this field, their attractive features, and, as appropriate, their shortcomings. This second edition summarizes some of the developments in this area which have occurred since the first edition of this book appeared in 2011. These include new results in the caloron/dyon picture of confinement, in functional approaches, and in studies of the Yang-Mills vacuum wave functional. Special attention, in two new chapters, is given to recent numerical investigations of the center vortex theory, and to the varieties of confinement which may exist in gauge-Higgs theories. Reviews of the first edition: "This is indeed a very good book. I enjoyed reading it and... I learned a lot from it.... It is definitely a research book that provides readers with a guide to the most updated confinement models." (Giuseppe Nardelli, Mathematical Reviews, Issue 2012 d) "The book is beautifully produced with special emphasis on the relevance of center symmetry and lattice formulation as well as an introduction to current research on confinement." (Paninjukunnath Achuthan, Zentralblatt MATH, Vol. 1217, 2011)

Table of Contents

. 1 Introduction . 2 Global Symmetry, Local Symmetry, and the Lattice . 2.1 Global Symmetry and the Ising Model . 2.2 Gauge Invariance: the Unbreakable Symmetry . 2.3 The Monte Carlo Method . 2.4 Possible Phases of a Gauge Theory References . 3 What Is Confinement? (Part I) . 3.1 Regge Trajectories, and the Spinning Stick Model . 3.2 The Fradkin-Shenker-Osterwalder-Seiler Theorem . 3.3 Remnant Gauge Symmetries . 3.3.1 Landau Gauge and the Kugo-Ojima Criterion . 3.3.2 Coulomb Confinement . 3.3.3 Remnant Symmetry Breaking . 3.4 Center Symmetry References . 4 Order Parameters for Confinement 4.1 The Wilson Loop 4.2 The Polyakov Loop 4.3 The 't Hooft Loop 4.4 The Vortex Free Energy 4.5 Summary References . 5 Properties of the Confining Force . References . 6 Center Vortices I - Basics . 6.1 The Mechanism (NEW) . 6.2 Center Gauges and Center Projection . 6.2.1 Direct Maximal Center Gauge . 6.2.2 Finding Thin Vortices . 6.2.3 Indirect Maximal Center Gauge . 6.2.4 Laplacian Center Gauge . 6.2.5 Direct Laplacian Center Gauge . 6.3 Numerical Investigations . 6.3.1 Center Dominance . 6.3.2 Vortex-Limited Wilson Loops . 6.3.3 Vortex Removal . 6.3.4 Scaling of the P-vortex Density . 6.3.5 Vortices at High Temperatures . 6.3.6 Chiral Condensates and Topological Charge . 6.3.7 Center Symmetry Breaking by Matter Fields . References . 7 Center Vortices II: Full, Vortex-only, and Vortex Removed Configurations (NEW) . 7.1 The smoothing procedure (NEW) . 7.2 The quark propagator (NEW) . 7.3 The gluon propagator (NEW) . 7.4 Instanton content (NEW) . 7.5 The spectrum (NEW) . References . 8 Confinement from Center Vortices III . 8.1 Casimir Scaling and Vortex Thickness . 8.2 What About "Gluon Confinement"? . 8.3 The Random Surface Model . 8.4 Vortices as Solitons . 8.5 Critique . References . 9 Monopoles, Calorons, and Dual Superconductivity . 9.1 Magnetic Monopoles in Compact QED . 9.2 The Georgi-Glashow Model in D=3 Dimensions . 9.3 Dual Superconductivity, and the Seiberg-Witten Model . 9.4 The Abelian Projection . 9.4.1 Monopoles and Vortices . 9.5 Calorons . 9.6 Critique: The problem of multiple winding Wilson loops (NEW) References . 10 Confinement in R3 x S1 (NEW) . 11 Coulomb Confinement . 11.1 The Gribov Horizon . 11.2 Coulomb Potential on the Lattice . 11.3 F-P Eigenvalue Density, and the Coulomb Self-Energy . 11.3.1 The Role of Center Vortices . 11.4 Critique . References . 12 Ghosts, Gluons, and Dyson-Schwinger Equations . 12.1 Dyson-Schwinger equations and the scaling solution . 12.2 Numerical results for ghost and gluon propagators . 12.3 The decoupling solution . 12.4 Landau gauge, BRST breaking, and non-positivity (NEW) . References . 13 Large-N, Planar Diagrams, and the Gluon-Chain Model . 13.1 Double-Line Notation and Factorization . 13.2 The Gluon Chain Model . 13.2.1 Numerical Investigation in Coulomb Gauge References . 14 The Vacuum Wavefunctional . 14.1 Dimensional Reduction . 14.2 Temporal Gauge Vacuum State in 2+1 Dimensions . 14.3 New Variables . References . 15 Anti-de Sitter Space and Confinement . 15.1 TheMaldacenaConjecture . 15.2 WilsonLoopsinAdSSpace . 15.3 AdS/QCD . References . 16 What is Confinement? (Part II) (NEW) . 16.1 Color confinement and separation-of-charge confinement in gauge theories with matter fields (NEW) . 16.2 Custodial symmetry breaking in Gauge-Higgs Theories (NEW) . 16.3 The role of the center revisited (NEW) . 17 ConcludingRemarks Index

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An introduction to the confinement problem

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