Strings to Strings: Yang-Mills Flux Tubes, QCD Strings and Effective String Theories

✍ Scribed by N. D. Hari Dass

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 468
• Category: Library

✦ Table of Contents

Preface
Contents
Acronyms
Part IThe Background
1 Elements to Elementary Particles
1.1 Introduction
1.2 The Elements
1.3 The Atoms
1.4 The Elementary Particles
1.4.1 The Spin Angular Momentum
1.4.2 Statistics and Spin
1.5 Quantum Electrodynamics
2 Radioactivity and Weak Interactions
2.1 Radioactivity
2.2 Energy Spectrum of β-Electrons
2.3 Wolfgang Pauli and the Neutrino
2.4 Fermi Theory of Beta Interactions
2.4.1 Neutrino Masses
2.4.2 Generalizing Fermi Theory
2.5 Even More Particles
2.6 Intermediate Vector Bosons
2.7 The Electroweak Unification
3 Nuclear Forces, Meson Field Theories and Their Failures
3.1 Nuclear Forces: Observational
3.2 Yukawa Theory
3.3 Meson Field Theories and Their Failures
3.4 Experimental Discoveries of the Pions
3.5 Meson Theories Post-Pion Discovery
Part IIHeisenberg’s S-matrix to String Theory
4 The S-matrix: From Heisenberg Till Now
4.1 Introduction
4.2 Kramers, Kronig and Analyticity
4.3 Connections to Causality
4.4 Causality and Analyticity in Non-relativistic Quantum Mechanics
4.5 Microcausality
5 QED: S-Matrix, Causality and Analyticity
5.1 Development of QED
5.2 Dyson Equivalence Proof
5.3 S-Matrix in QED
5.4 Causality, Analyticity, and S-Matrix in Non-perturbative RQFT
6 A Non-perturbative RQFT Primer
6.1 QFT-A Particle Perspective
6.1.1 Notations and Conventions
6.2 Quantum Fields from Particles
7 The Kallen-Lehmann Representation
7.1 Introduction
7.2 The Kallen-Lehmann Representation
7.2.1 Lessons for Analytic S-Matrix
8 The Lehmann Symanzik Zimmermann (LSZ) Formalism
8.1 The LSZ Reduction Formulae
8.1.1 The Retarded Commutator Representation
8.1.2 What if No Tricks are Used?
8.1.3 Unretarded Commutator Representation
8.1.4 Crossing Symmetry
9 Unitarity and the LSZ Formalism
9.1 Introduction
9.2 General Considerations
9.3 LSZ Formalism and Unitarity
9.3.1 Proof of Unitarity in LSZ Formalism
10 Lehmann Ellipses
10.1 Lehmann Ellipses
10.1.1 Jost-Lehmann-Dyson Theorem
11 Dispersion Relations in RQFT
11.1 Introduction
11.2 Toll's Analysis of the Logical Foundations
11.3 Dispersion Relations in QFT: General Considerations
11.4 Forward Scattering Dispersion Relations
11.4.1 Massless Particle Scattering
11.4.2 Massive Particle Scattering: Goldberger Analysis
11.4.3 Massive Particle Scattering: Symanzik Analysis
11.5 Non-forward Scattering: Salam's Approach
11.6 Fixed-t Dispersion Relations: Lehmann and Sommer
11.7 Mandelstam Double Spectral Representation
12 Some Uses and Applications of Analyticity and Dispersion Relations
12.1 Low Energy Meson-Nucleon Scattering
12.2 Pion Decay
12.3 The Froissart, Khuri-Kinoshita Bounds
12.3.1 The Pomeranchuk Theorem
12.3.2 Pi-Pi Scattering
12.3.3 Some Recent Developments
12.4 Adler-Weisberger Relations for gA
13 In the Land of Complex Angular Momentum
13.1 Introduction
13.2 Lehmann Ellipses and Partial-wave Analysis
13.3 Going Beyond Lehmann Ellipses: Complex Angular Momentum
13.3.1 Cases where Angular Momentum can be Complexified
13.4 The Sommerfeld-Watson Transform
13.5 Regge Poles and Their Properties
13.5.1 Bound States and Resonances
13.5.2 Regge Asymptotics
14 Superconvergence Relations, FESR and Duality
14.1 Introduction
14.2 Superconvergence Relations
14.2.1 Igi's Significant Next Step
14.3 Finite Energy Sum Rules(FESR)
14.3.1 Horn-Schmid Formulation
14.3.2 Dolen, Horn, Schmid Elaboration
14.3.3 Igi-Matsuda FESR
14.4 Alarm Bells Regarding FESR
14.4.1 The Mandula-Slansky Work
14.4.2 Fujisaki's Work
14.5 Concluding Remarks
15 The Veneziano Formula and the Dual Resonance Model
15.1 Introduction
15.2 The Veneziano Formula
15.2.1 Veneziano's Motivation
15.2.2 Important Properties of the Veneziano Formula-I
15.2.3 Precise Duality
15.2.4 The Issue of Daughters
15.3 The Multi-point Function Generalizations
15.3.1 The 5-Point Function
15.4 The Higher Point Functions
15.4.1 The 6-Point Function
15.4.2 N-point Function
15.4.3 Koba-Nielsen Variables
16 The Operator Formalism and The Dual Resonance Model
16.1 Introduction
16.2 Operator Formalism-I
16.2.1 Preliminaries
16.2.2 Oscillators and N-Point Functions
16.2.3 Factorizability and Degeneracies
16.3 Operator Formalism-II
16.4 Physical States of the Dual Resonance Models
16.4.1 Varieties of States of the Dual Model
16.4.2 Absence of Ghosts and DDF Construction
16.4.3 QED Revisited
16.4.4 First Two Excited States
16.5 The Shapiro-Virasoro Model
17 The Birth of String Theory
17.1 Introduction
17.2 Emergent Strings and Their Actions
17.2.1 Nielsen-Susskind Action
17.2.2 Nambu-Goto Action
17.3 Classical Analysis of the Nambu-Goto Action
17.3.1 Light-Cone Parametrization
17.3.2 Non-covariant Quantization
17.4 Covariant Quantization
17.5 The Arvis Quantization
17.6 Path Integral Quantizations
Part IIIStrings Lost: QCD, The Field Theory of Strong Interactions
18 Effective Field Theories
18.1 Introduction
18.2 Effective Description of Weak Interactions
18.3 Effective Descriptions of Superconductivity
18.4 Effective Descriptions of Strong Interactions
18.4.1 Group Structure of Chiral Transformations
18.4.2 Spontaneous Breaking of Chiral Symmetry
18.4.3 Non-linear Realization of Chiral Symmetry
18.4.4 Chiral Cancellations
18.4.5 Finite Pion Mass
18.4.6 Phenomenological Lagrangeans
18.4.7 Chiral Perturbation Theory
18.4.8 Anomalous Sector
19 Quantum Chromodynamics (QCD)—A RQFT for Strong Interactions
19.1 Introduction
19.2 Historical Backgrounds to QCD
19.2.1 Strangeness
19.2.2 Sakata Model
19.2.3 The Eightfold Way
19.3 The Quark Models
19.3.1 Gell-Mann-Zweig Quark Models
19.3.2 The Statistics Difficulties
19.3.3 Han-Nambu (HN) Quark Model
19.3.4 π0-Decay as a Test for Quark Models
19.3.5 Colour in Gell-Mann-Zweig Model
19.4 Towards Theories of Quark Dynamics
19.4.1 Han-Nambu Approach
19.4.2 Fritzsch-Gell-Mann Approach
19.4.3 Observational Tests for Han-Nambu Model Revisited
19.4.4 Deep Inelastic Scattering
19.5 Quantum Chromodynamics (QCD)
19.5.1 A QED Interlude
19.5.2 QCD
19.6 Asymptotic Freedom and Perturbation Theory
19.6.1 Sliding Scales and Running Couplings
19.6.2 The Callan-Symanzik Equation and the Beta Function
19.6.3 The Running Couplings
19.6.4 The Beta Function
19.6.5 RG in QED
19.6.6 Improving Perturbation Theory
19.6.7 RG in QCD
19.6.8 Higher Order Beta Functions
19.6.9 More on Asymptotic Freedom
19.7 The Static Quark-Antiquark Potential in QCD
19.8 Colour Confinement in QCD
19.9 QCD and Chiral Symmetry
20 Essentials of Lattice Gauge Theories (LGT)
20.1 Introduction
20.2 An Elementary Introduction to Lattice Field Theories
20.2.1 The Statistical Continuum Limit
20.2.2 Statistical Continuum Limit of the D=1 Example
20.3 Gauge Fields on Lattices
20.3.1 Abelian Gauge Fields
20.4 Non-Abelian Gauge Fields on Lattice
20.4.1 Invariants of Non-Abelian Gauge Theories
20.4.2 Wegner-Wilson Loops
20.4.3 Polyakov Lines (Loops)
20.4.4 The Plaquette Action
20.4.5 The LGT Path-Integral
Part IVStrings Regained: From Yang-Mills Flux Tubes to Effective String Theories
21 Lattice Gauge Theory and Yang-Mills Flux Tubes
21.1 Introduction
21.2 Flux Tube Observables
21.2.1 The Static QbarQ-Potential
21.2.2 Confinement Criterion
21.2.3 The Polyakov Lines (Loops)
21.2.4 The Flux Tube Profile
21.3 Creutz's Pioneering Numerical Works
21.3.1 Monte Carlo Simulations
21.3.2 The Statistical Continuum Limit
21.4 Work of Ambjorn, Olesen and Peterson
21.5 Flux Profile Studies
21.6 Simulations of Lüscher and Weisz
21.7 Simulations of Hari Dass and Pushan Majumdar
22 Flux Tubes and Effective String Theories (EST)
22.1 Introduction
22.2 Lüscher-Weisz Effective String Theories
22.2.1 Leading Order Analysis
22.2.2 A Possible Boundary Term
22.2.3 Dimension-2 Corrections
22.2.4 Open-Closed String Duality
22.2.5 Purely Classical Analysis
22.3 Polchinski-Strominger(PS) Effective String Theory
22.3.1 Leading Order Analysis of PS Effective Actions
22.4 PS Effective String Theories for all D
22.4.1 Order R-3 Corrections to the Spectrum
22.4.2 Ground State Momentum Revisited
22.5 Covariant Calculus for Effective String Theories
22.5.1 Covariant Calculus I: The Nambu-Goto way
22.5.2 Covariant Calculus II: The Polyakov Way
22.5.3 Weyl Connections and Weyl-Weight Compensators
22.6 Gauge Fixing the Covariant Actions
22.6.1 The Static Gauge
22.6.2 Covariant Calculus I: The Conformal Gauge
22.6.3 Covariant Calculus II: The Conformal Gauge
22.7 Equivalence of Conformal Gauges
22.8 Drummond Actions as Examples
22.9 Spectrum of Effective Strings at Even Higher Orders
22.9.1 Results by Aharony et al.
22.9.2 Alleged Equivalence to Arvis Spectrum To All Orders
22.10 Other Important Issues
22.10.1 The Excited States
22.10.2 AdS-CFT Approaches
22.10.3 Thickness of Flux Tubes
22.11 Path Integral Quantization of Subcritical Strings
22.12 Concluding Remarks
Index
Index