Nonperturbative topological phenomena in QCD and related theories / Edward Shuryak.

Format:

Book

Author/Creator:

Shuryak, E. V., author.

Series:

Lecture notes in physics ; 977.

Lecture Notes in Physics ; 977

Language:

English

Subjects (All):

Quantum chromodynamics.

Gauge fields (Physics).

Quantum field theory.

Physical Description:

1 online resource (529 pages).

Edition:

1st ed.

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This book introduces a variety of aspects in nonperturbative Quantum Chromodynamics (QCD), focusing on the topological objects present in gauge theories.These objects, like magnetic monopoles, instantons, instanto-dysons, sphalerons, QCD flux tubes, etc, are first introduced individually and, later, treated collectively.

Contents:

Intro

Preface

Acknowledgments

Contents

Notations and Units

Some Abbreviations Used

Units

Space-Time and Other Indices, Standard Gamma Matrices

Angular Momentum in Four Dimensions and t'Hooft η Symbol

About the Author

1 Introduction

1.1 What Are the ``Nonperturbative Topological Phenomena''?

1.2 Brief History of Non-Abelian Gauge Theories and Quantum Chromodynamics

1.3 Introduction to Chiral Symmetries and Their Breaking

1.3.1 Spontaneous Breaking of the SU(Nf)A Symmetry

1.3.2 The Fate of U(1)A Symmetry

1.4 Introduction to Color Confinement

1.4.1 Polyakov Lines

1.4.2 Wilson Lines and Vortices

1.4.3 Hadronic Matter at T&lt

Tc and the Hagedorn Phenomenon

1.5 Particle-Monopoles, Including the Real-Time (Minkowskian) Applications

1.6 Instantons and Its Constituents, the Instanton-Dyons

1.7 Interrelation of Various Topology Manifestations and the Generalized Phase Diagrams

1.8 Which Quantum Field Theories Will We Discuss?

References

2 Monopoles

2.1 Magnetic Monopoles in Electrodynamics

2.2 The Non-Abelian Gauge Fields and t' Hooft-Polyakov Monopole

2.3 Polyakov's Confinement in Three Dimensions

2.4 Electric-Magnetic Duality

2.5 Lattice Monopoles in QCD-like Theories

2.6 Brief Summary

3 Monopole Ensembles

3.1 Classical Charge-Monopole Dynamics

3.2 Monopole Motion in the Field of Several Charges

3.3 Strongly Coupled QGP as a ``Dual'' Plasma with Monopoles

3.4 Jet Quenching Due to Jet-Monopole Scattering

3.5 Quantum-Mechanical Charge-Monopole Scattering Problem

3.6 Quark and Gluon Scattering on Monopoles and Viscosity of QGP

3.7 Transport Coefficients from Binary Quantum Scattering

3.8 Monopoles and the Flux Tubes

3.8.1 Flux Tubes on the Lattice, at Zero T, and Near Tc.

3.8.2 Does the Tc Indeed Represent the Monopole Condensation Temperature?

3.8.3 Constructing the Flux Tubes in the ``Normal'' Phase

3.9 Lattice Studies of the Bose-Einstein Condensation of Monopoles at the Deconfinement Transition

3.10 Quantum Coulomb Gases Studied by Path Integral Monte Carlo (PIMC)

3.11 Brief Summary

4 Fermions Bound to Monopoles

4.1 Fermionic Zero Modes

4.2 Chiral Symmetry Breaking by Monopoles

4.3 More on Fermions Bound to Monopoles, in the SUSY World and Perhaps Beyond

4.4 Brief Summary

5 Semiclassical Theory Based on Euclidean Path Integral

5.1 Euclidean Path Integrals and Thermal Density Matrix

5.1.1 Generalities

5.1.2 The Harmonic Oscillator

5.2 Euclidean Minimal Action (Classical) Paths: Fluctons

5.3 Quantum/Thermal Fluctuations in One Loop

5.4 Two and More Loops

5.5 Path Integrals and the Tunneling

5.6 The Zero Modes and the Dilute Instanton Gas

5.7 Quantum Fluctuations Around the Instanton Path

5.8 Transseries and Resurgence

5.9 Complexification and Lefschetz Thimbles

5.9.1 Elementary Examples Explaining the Phenomenon

5.9.2 Quasi-Exactly Solvable Models and the Necessity of Complex Saddles

5.10 Brief Summary

6 Gauge Field Topology and Instantons

6.1 Chern-Simons Number and Topologically Nontrivial Gauges

6.2 Tunneling in Gauge Theories and the BPST Instanton

6.2.1 The Theta-Vacua

6.2.2 The One-Loop Correction to the Instanton: The Bosonic Determinant

6.2.3 Propagators in the Instanton Background

6.2.4 The Exact NSVZ Beta Function for Supersymmetric Theories

6.2.5 Instanton-Induced Contribution to the Renormalized Charge

6.3 Single Instanton Effects

6.3.1 Quarkonium Potential and Scattering Amplitudes

6.4 Fermionic Transitions During Changes of Gauge Topology.

6.4.1 The Fermionic Zero Mode of the Instanton

6.4.2 Electroweak Instantons Violate Baryon and Lepton Numbers

6.4.3 Instanton-Induced ('t Hooft) Effective Lagrangian

6.4.4 Instanton-Induced Quark Anomalous Chromomagnetic Moment

6.4.5 Instanton-Induced Diquark-Quark Configurations in the Nucleon

6.4.6 Instanton-Induced Decays of ηc and Scalar/Pseudoscalar Glueballs

6.4.7 Instanton-Induced Spin Polarization in Heavy Ion Collisions

6.5 Brief Summary

7 Topology on the Lattice

7.1 Global Topology: The Topological Susceptibility and the Interaction Measure

7.2 ``Lattice Cooling'' and Instantons

7.3 A ``Constrained Cooling'': Preserving the Polyakov Line Value

7.4 Brief Summary

8 Instanton Ensembles

8.1 Qualitative Introduction to the Instanton Ensembles

8.2 The Dilute Gas of Individual Instantons

8.3 The ``Instanton Liquid Model'' (ILM)

8.4 Statistical Mechanics of the Instanton Ensembles

8.4.1 Instanton Ensemble in the Mean Field Approximation (MFA)

8.4.2 Diquarks and Color Superconductivity

8.4.3 Instantons for Larger Number of Colors

8.5 Brief Summary

9 QCD Correlation Functions and Topology

9.1 Generalities

9.1.1 Definitions and an Overall Picture

9.1.2 Small Distances: Perturbative Normalization of the Correlators

9.1.3 Dispersion Relations and Sum Rules

9.1.4 Flavor and Chirality Flow: Combinations of Correlators

9.1.5 General Inequalities Between the One-Quark-Loop Correlators

9.2 Vector and Axial Correlators

9.3 The Pseudoscalar Correlators

9.4 The First Order in the 't Hooft Effective Vertex

9.5 Correlators in the Instanton Ensemble

9.5.1 Mesonic Correlators

9.5.2 Baryonic Correlation Functions

9.6 Comparison to Correlators on the Lattice

9.7 Gluonic Correlation Functions

9.8 Wave Functions.

9.9 Brief Summary

10 Light-Front Wave Functions, Exclusive Processes and Instanton-Induced Quark Interactions

10.1 Quark Models of Hadrons

10.2 Light-Front Observables

10.3 Quark Models on the Light Front: Mesons in the q Sector

10.4 Quark Models on the Light Front: Baryons as qqq States

10.5 Quark Models on the Light Front: Pentaquarks and the Five-Quark Sector of Baryons

10.6 Hard and Semihard Exclusive Processes

10.6.1 Vector Form Factors of the Pseudoscalar Mesons

10.6.2 Scalar Form Factors of the Pseudoscalar Mesons

10.6.3 Form Factors of Transversely Polarized Vector Mesons

10.7 Brief Summary

11 The Topological Landscape and the Sphaleron Path

11.1 The Sphalerons

11.2 Instanton-Antiinstanton Interaction and the ``Streamline'' Set of Configurations

11.3 From the Instanton-Antiinstanton Configurations to the Sphaleron Path

11.4 The Sphaleron Path from a Constrained Minimization

11.5 Sphaleron Explosions

11.6 Chiral Anomaly and Sphaleron Explosions

11.7 Brief Summary

12 Sphaleron Transitions in Big and Little Bangs

12.1 Electroweak Sphalerons and Primordial Baryogenesis

12.1.1 Introduction to Cosmological Baryogenesis

12.1.2 Electroweak Phase Transition

12.1.3 Sphaleron Size Distribution

12.1.4 The Hybrid (Cold) Cosmological Model and Sphalerons

12.1.5 Effective Lagrangian for CP Violation

12.1.6 The CP Violation in the Background of Exploding Sphalerons

12.1.7 Electroweak Sphaleron Explosion: Other Potential Observables

12.2 QCD Sphalerons

12.2.1 Sphaleron Transitions at the Initial Stage of Heavy Ion Collisions

12.2.2 Sphalerons from Instant Perturbations

12.2.3 QCD Sphalerons in Experiments

12.2.4 Diffractive Production of Sphalerons

12.3 Brief Summary

13 Chiral Matter.

13.1 Examples of Chiral Matter

13.2 Electrodynamics in a CP-Violating Matter

13.3 Chiral Magnetic Effect (CME) and the Chiral Anomaly

13.4 Chiral Vortical Effect

13.5 The Chiral Waves

13.6 Brief Summary

14 Instanton-Dyons

14.1 The Polyakov Line and Confinement

14.1.1 Generalities

14.1.2 The Free Energy of the Static Quark on the Lattice

14.1.3 The Color Phases

14.2 Semiclassical Instanton-Dyons

14.2.1 The Instanton-Dyon Field Configuration

14.3 Instanton-Dyon Interactions

14.3.1 Large-Distance Coulomb

14.3.2 The Dyon-Antidyon Classical Interaction

14.3.2.1 Combing the Hedgehogs

14.3.2.2 Following the Gradient Flow Down the Streamline

14.4 The Partition Function in One Loop

14.4.1 Electric Screening

14.4.2 The One-Loop Measure, Perturbative Coulomb Corrections and the ``Core''

14.5 Fermionic Zero Modes

14.5.1 How Quark Zero Modes Are Shared Between the Dyons

14.5.2 The Zero Mode for the Fundamental Fermion

14.5.2.1 Elements of Quark ``Hopping Matrix''

14.5.3 Fermionic Zero Mode for a Set of Self-Dual Dyons

14.6 Instanton-Dyons on the Lattice Are Seen via Their Fermionic Zero Modes

14.7 Brief Summary

15 Instanton-Dyon Ensembles

15.1 Deformed QCD and Dilute Ensembles with Confinement

15.1.1 Perturbative Holonomy Potential and Deformed QCD

15.1.2 The Instanton-Dyons in Na=1 QCD(or N=1 SYM)

15.1.3 QCD(adj) with Na&gt

1 at Very Small Circle: Dilute Molecular (or ``bion'') Ensembles

15.1.4 QCD(adj) with Na=2 and Periodic Compactification on the Lattice

15.2 Dense Dyon Plasma in the Mean Field Approximation

15.3 Statistical Simulations of the Instanton-Dyon Ensembles

15.3.1 Holonomy Potential and Deconfinement in Pure Gauge Theory

15.3.2 Instanton-Dyon Ensemble and Chiral Symmetry Breaking.

15.4 QCD with Flavor-Dependent Quark Periodicity Phases.

Notes:

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

3-030-62990-2

OCLC:

1244536130