The Phases of Quantum Chromodynamics : From Confinement to Extreme Environments (Cambridge Monographs on Particle Physics, Nuclear Physics and Cosmology)

Half-title......Page 3
Series-title......Page 4
Title......Page 5
Copyright......Page 6
Contents......Page 7
1 Introduction......Page 11
2.1 Notation and definitions and critical indices......Page 20
2.2 Correlation-length scaling and universality classes......Page 24
2.3 Properties of the Ising model......Page 27
2.4 The Kosterlitz–Thouless model......Page 29
2.5 Coulomb gas, duality maps, and the phases of the planar model......Page 34
2.6 Asymptotic freedom in two-dimensional spin systems......Page 40
2.7 Instantons in two-dimensional spin systems......Page 46
2.8 Computer experiments and simulation methods......Page 47
2.9 The transfer matrix in field theory and statistical physics......Page 51
2.9.1 The simple harmonic oscillator......Page 52
2.9.2 The transfer matrix for the Ising model......Page 56
2.9.3 Self-duality and kink condensation through the eyes of the transfer matrix......Page 59
3.1 Lattice formulation, local gauge invariance, and the continuum action......Page 63
3.2 Confinement and the strong-coupling limit......Page 67
3.3 Confinement mechanisms in two and four dimensions: vortex and monopole condensation......Page 73
4.1 Asymptotic freedom and the continuum limit......Page 84
4.2 Axial symmetries and the vacuum of QCD......Page 86
4.3 Two-dimensional fermionic models of confinement, axial symmetries, and Theta vacua......Page 87
4.4 Instantons and the scales of QCD......Page 94
5.1 Free fermions on the lattice in one and two dimensions......Page 103
5.2 Fermions and bosons on Euclidean lattices......Page 111
5.3 Staggered Euclidean fermions......Page 114
5.4 Block derivatives and axial symmetries......Page 117
5.5 Staggered fermions and remnants of chiral symmetry......Page 119
5.6.1 Domain-wall fermions......Page 121
5.6.2 The Ginsparg–Wilson relation......Page 125
5.7 Chiral-symmetry breaking on the lattice......Page 127
5.8 Simulating dynamical fermions in lattice-gauge theory......Page 136
5.9 The microcanonical ensemble and molecular dynamics......Page 137
5.10 Langevin and hybrid algorithms......Page 142
6.1 Continuous time and discrete space......Page 146
6.2 Quark confinement in Hamiltonian lattice-gauge theory and thin strings......Page 155
6.3 Relativistic thin strings, delocalization, and Casimir forces......Page 156
6.4 Roughening and the restoration of spatial symmetries......Page 160
7.1 Finite-temperature transitions at strong coupling......Page 168
7.2 Simulations at nonzero temperature......Page 172
7.3 Pure gauge-field simulations at nonzero temperature......Page 175
7.4 Restoration of chiral symmetry and high temperature......Page 180
7.5 Hadronic screening lengths......Page 182
7.6 Thermal dilepton rates and experimental signatures for the quark–gluon plasma......Page 184
7.7 A tour of the three-flavor QCD phase diagram......Page 186
8.1 The thermodynamic background......Page 192
8.1.1 Thermodynamic ensembles......Page 193
8.1.2 The partition function and Lagrangian......Page 195
8.1.3 Conserved charge and chemical potential......Page 196
8.1.4 The grand canonical partition function and Lagrangian......Page 198
8.1.5 Derivatives of the partition function......Page 200
8.1.6 An example: fermions......Page 201
8.1.7 An example: bosons......Page 208
8.2 Hadron phenomenology and simple models of the transition to the quark–gluon plasma......Page 212
8.3 A tour of the Tau–Mu phase diagram......Page 217
8.3.1 Symmetry, order parameters, and phase transitions......Page 218
8.3.2 Definitions......Page 220
8.3.3 Zero temperature......Page 222
8.3.4 Finite Tau and Mu......Page 226
8.3.5 Universal properties of the tricritical point......Page 229
8.3.6 Summary and remarks......Page 232
8.4 The quark–gluon plasma and the energy scales of QCD......Page 233
8.5 The extreme environment at a relativistic heavy-ion collider......Page 236
9.1 Color superconductivity and color–flavor locking......Page 246
9.2 Calculating the gap at asymptotically large Mu......Page 249
9.2.1 The effective action for quarks near the Fermi surface......Page 250
9.2.2 The strategy of the calculation and the meaning of the gap......Page 253
9.2.3 The gap equation......Page 256
9.3 Lowest excitations of the CFL phase......Page 270
9.3.1 The effective Lagrangian for Goldstone modes......Page 272
9.3.2 Decay constants of the Goldstone bosons......Page 275
9.3.3 Meson masses......Page 279
9.3.4 Continuity of quark and nuclear matter?......Page 286
9.4 Comments and some further developments......Page 288
10.1 QCD at finite Mu and the sign problem......Page 290
10.2 The random-matrix model of QCD......Page 292
10.2.1 A random-matrix-model description of the QCD phase diagram......Page 293
10.2.2 Chiral-symmetry breaking, Lee–Yang zeros, and an electrostatic analogy......Page 299
10.2.3 The quenched limit of QCD and the random-matrix model......Page 301
10.3 Two-color QCD and effective Lagrangians......Page 305
10.3.1 QCD inequalities and the nature of the ground state......Page 307
10.3.2 Symmetries and Goldstone bosons in the diquark phase......Page 308
10.3.3 Effective-Lagrangian construction......Page 310
10.3.4 Vacuum alignment, diquark condensation, the phase diagram, and scaling laws......Page 313
10.4 QCD at nonzero isospin chemical potential......Page 317
10.4.2 Small isospin densities: the pion condensate......Page 318
10.4.3 Asymptotically high isospin densities: the quark–antiquark condensate......Page 322
10.4.4 Quark–hadron continuity and confinement......Page 323
10.5 Pion propagation near and below Tauc......Page 326
10.5.1 Pion dispersion from static quantities (summary)......Page 327
10.5.2 Derivation......Page 328
10.5.3 Critical behavior......Page 330
11.1 Propagators and formulating the chemical potential on a Euclidean lattice......Page 334
11.2 Naive fermions at finite density......Page 336
11.3 The three-dimensional four-Fermi model at nonzero Tau and Mu......Page 340
11.4 Four-flavor SU(2) lattice-gauge theory at nonzero Mu and Tau......Page 345
11.5 High-density QCD and static quarks......Page 355
11.6 The Glasgow algorithm......Page 357
11.7 The Fodor–Katz method for high Tau, low Mu......Page 359
11.8 QCD at complex chemical potential......Page 360
12 Epilogue......Page 365
References......Page 367
Index......Page 373