String Theory in a Nutshell

Name: String Theory in a Nutshell | Second Edition
Brand: Princeton University Press
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Second Edition

Elias Kiritsis(Author)

Princeton University Press

2nd Edition

Published on 16. April 2019

888 pages

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Content

Cover
Contents
Preface to the Second Edition
Preface to the First Edition
Abbreviations
1. Introduction
1.1 Prehistory
1.2 The Case for String Theory
1.3 A Stringy Historical Perspective
1.4 Conventions
1.5 A Brief Guide to the Literature
2. Classical String Theory
2.1 The Point Particle
2.2 Relativistic Strings
2.3 Oscillator Expansions
2.3.1 Closed Strings
2.3.2 Open Strings
2.3.3 The Virasoro Constraints
Further Reading
Exercises
3. Quantization of Bosonic Strings
3.1 Covariant Canonical Quantization
3.2 Light-Cone Quantization
3.3 Spectrum of the Bosonic String
3.4 Unoriented Strings
3.4.1 Open Strings and Chan-Paton Factors
3.5 Path Integral Quantization
3.6 Topologically Nontrivial Worldsheets
3.7 BRST Primer
3.8 BRST in String Theory and the Physical Spectrum
Further Reading
Exercises
4. Conformal Field Theory
4.1 Conformal Transformations
4.1.1 The Case of Two Dimensions
4.2 Conformally Invariant Field Theory
4.3 Radial Quantization
4.4 Mode Expansions
4.5 Virasoro Algebra and the Central Charge
4.6 Hilbert Space
4.7 The Free Boson
4.8 The Free Fermion
4.9 The Conformal Anomaly
4.10 Representations of the Conformal Algebra
4.11 Affine Current Algebras
4.12 Free Fermions and O(N) Affine Symmetry
4.13 Superconformal Symmetry
4.13.1 N =(1, 0)2 Superconformal Symmetry
4.13.2 N =(2, 0)2 Superconformal Symmetry
4.13.3 N =(4, 0)2 Superconformal Symmetry
4.14 Scalars with Background Charge
4.15 The CFT of Ghosts
4.16 CFT on the Disk
4.16.1 Free Massless Bosons on the Disk
4.16.2 Free Massless Fermions on the Disk
4.16.3 The Projective Plane
4.17 CFT on the Torus
4.18 Compact Scalars
4.18.1 Modular Invariance
4.18.2 Decompactification
4.18.3 The Torus Propagator
4.18.4 Marginal Deformations
4.18.5 Multiple Compact Scalars
4.18.6 Enhanced Symmetry and the String Brout-Englert-Higgs Effect
4.18.7 T-Duality
4.19 Free Fermions on the Torus
4.20 Bosonization
4.20.1 "Bosonization" of Bosonic Ghost Systems
4.21 Orbifolds
4.22 CFT on Other Surfaces of Euler Number Zero
4.22.1 The Cylinder (Annulus)
4.22.2 The Klein Bottle
4.22.3 The Möbius Strip
4.23 CFT on Higher-Genus Riemann Surfaces
Further Reading
Exercises
5. Scattering Amplitudes and Vertex Operators
5.1 Physical Vertex Operators
5.2 Calculation of Tree-Level Tachyon Amplitudes
5.2.1 The Closed String
5.2.2 The Open String
5.3 The One-Loop Vacuum Amplitudes
5.3.1 The Torus
5.3.2 The Cylinder
5.3.3 The Klein Bottle
5.3.4 The Möbius Strip
5.3.5 Tadpole Cancellation
5.3.6 UV Structure and UV-IR Correspondence
Further Reading
Exercises
6. Strings in Background Fields
6.1 The Non linear s-Model Approach
6.2 The Quest for Conformal Invariance
6.3 Linear Dilaton and Strings in D&26 Dimensions
6.4 T-Duality in Nontrivial Backgrounds
Further Reading
Exercises
7. Superstrings and Supersymmetry
7.1 N =(1, 1)2 Worldsheet Superconformal Symmetry
7.2 Closed (Type-II) Superstrings
7.2.1 Massless R-R States
7.3 Type-I Superstrings
7.4 Heterotic Superstrings
7.5 Superstring Vertex Operators
7.5.1 Open-Superstring Vertex Operators
7.5.2 Type-II Superstring Vertex Operators
7.5.3 Heterotic String Vertex Operators
7.6 One-Loop Superstring Vacuum Amplitudes
7.6.1 Type-IIA/B Superstrings
7.6.2 Heterotic Superstrings
7.6.3 Type-I Superstrings
7.7 Closed Superstrings and T-Duality
7.7.1 Type-II String Theories
7.7.2 Heterotic strings
7.8 Supersymmetric Effective Actions
7.9 Anomalies
Further Reading
Exercises
8. D-Branes
8.1 Antisymmetric Tensors and p-Branes
8.2 Open Strings and T-Duality
8.3 D-Branes
8.4 D-Branes and R-R Charges
8.4.1 D-Instantons
8.5 D-Brane Effective Actions
8.5.1 The Dirac-Born-Infeld Action
8.5.2 Anomaly-Related Terms
8.6 Multiple Branes and Non-Abelian Symmetry
8.7 T-Duality and Orientifolds
8.8 D-Branes as Supergravity Solitons
8.8.1 Supergravity Solutions
8.8.2 Horizons and Singularities
8.8.3 Extremal Branes and Their Near-Horizon Geometry
8.9 NS5-Branes
Further Reading
Exercises
9. Compactification and Supersymmetry Breaking
9.1 Narain Compactifications
9.2 Worldsheet versus Spacetime Supersymmetry
9.2.1 N =14 Spacetime Supersymmetry
9.2.2 N =24 Spacetime Supersymmetry
9.3 Orbifold Reduction of Supersymmetry
9.4 A Heterotic Orbifold with N =24 Supersymmetry
9.5 Spontaneous Supersymmetry Breaking
9.6 A Heterotic N =14 Orbifold and Chirality in Four Dimensions
9.7 Calabi-Yau Manifolds
9.7.1 Holonomy
9.7.2 Consequences of SU(3) Holonomy
9.7.3 The CY Moduli Space
9.8 N=14 Heterotic Compactifications
9.8.1 The Low-Energy N =14 Heterotic Spectrum
9.9 K3 Compactification of Type-II Strings
9.10 N =26 Orbifolds of Type-II Strings
9.11 CY Compactifications of Type-II Strings
9.12 Mirror Symmetry
9.13 Absence of Continuous Global Symmetries
9.14 Orientifolds
9.14.1 K3 Orientifolds
9.14.2 The Klein Bottle Amplitude
9.14.3 D-Branes on T4/Z2
9.14.4 The Cylinder Amplitude
9.14.5 The Möbius Strip Amplitude
9.14.6 Tadpole Cancellation
9.14.7 The Open-String Spectrum
9.15 D-Branes at Orbifold Singularities
9.16 Magnetized Compactifications and Intersecting Branes
9.16.1 Open Strings in an Internal Magnetic Field
9.16.2 Intersecting Branes
9.16.3 Intersecting D6-Branes
9.17 Where Is the Standard Model?
9.17.1 The Heterotic String
9.17.2 Type-II String Theory
9.17.3 The Type-I String
9.18 Unification
Further Reading
Exercises
10. Loop Corrections to String Effective Couplings
10.1 Calculation of Heterotic Gauge Thresholds
10.2 On-Shell IR Regularization
10.2.1 Evaluation of Thresholds
10.3 Heterotic Gravitational Thresholds
10.4 One-Loop Fayet-Iliopoulos Terms
10.5 N =1, 24 Examples of Threshold Corrections
10.6 N =24 Universality of Thresholds
10.7 Unification Revisited
Further Reading
Exercises
11. Duality Connections and Nonperturbative Effects
11.1 Perturbative Connections
11.2 BPS States and BPS Bounds
11.3 Nonrenormalization Theorems and BPS-Saturated Couplings
11.4 Type-IIA versus M-Theory
11.5 Self-Duality of the Type-IIB String
11.6 U-Duality of Type-II String Theory
11.6.1 U-Duality and Bound States
11.7 Heterotic/Type-I Duality in Ten Dimensions
11.7.1 The Type-I D1 String
11.7.2 The Type-I D5-Brane
11.7.3 Further Consistency Checks
11.8 M-Theory and the E8 × E8 Heterotic String
11.8.1 Unification at Strong Heterotic Coupling
11.9 Heterotic/Type-II Duality in Six Dimensions
11.9.1 Gauge Symmetry Enhancement and Singular K3 Surfaces
11.9.2 Heterotic/Type-II Duality in Four Dimensions
11.10 Conifold Singularities and Conifold Transitions
11.11 D7-Branes and F-Theory
Further Reading
Exercises
12. Compactifications with Fluxes
12.1 Toy Models
12.1.1 A Six-Dimensional Freund-Rubin-Like Compactification
12.1.2 Type-IIA Flux Compactifications
12.2 Freund-Rubin Compactifications of M-Theory
12.3 (Partial) Supersymmetry Breaking in Flux Compactifications
12.3.1 Magnetic Flux Quantization
12.3.2 Supersymmetry in the Absence of Fluxes
12.3.3 Supersymmetry in the Presence of Fluxes and G-Structures
12.3.4 Reduction of Type-IIB Killing Spinor Equations
12.3.5 Diracology and Primitivity on Manifolds of SU(3) Holonomy
12.4 N =1 IIB Flux Compactifications
12.4.1 Special Solutions
12.4.2 The Moduli Superpotential
12.5 The Landscape of Vacua and the Cosmological Constant
12.5.1 Ensembles of String Vacua
12.6 Outlook
Further Reading
Exercises
13. Black Holes and Entropy in String Theory
13.1 A Brief History
13.2 The Strategy
13.3 Black-Hole Thermodynamics
13.3.1 The Euclidean Continuation
13.3.2 Hawking Evaporation and Graybody Factors
13.4 The Information Problem and the Holographic Hypothesis
13.5 Five-Dimensional Extremal Charged Black Holes
13.6 Five-Dimensional Nonextremal RN Black Holes
13.7 The Near-Horizon Region
13.8 Semi-classical Derivation of the Hawking Rate
13.9 The Microscopic Realization
13.9.1 The World-Volume Theory of the Bound State
13.9.2 The Low-Energy SCFT of the D1-D5 Bound States
13.9.3 Microscopic Calculation of the Entropy
13.9.4 Microscopic Derivation of Hawking Evaporation Rates
13.10 Hints of Holography
13.11 The Firewall Paradox
Further Reading
Exercises
14. The Bulk/Boundary (Holographic) Correspondence
14.1 Large-N Gauge Theories and String Theory
14.2 The Decoupling Principle
14.3 The Near-Horizon Limit
14.4 Elements of the Correspondence
14.5 Bulk Fields and Boundary Operators
14.6 Holography
14.7 Testing the AdS5/CFT4 Correspondence
14.7.1 The Chiral Spectrum of N =44 Gauge Theory
14.7.2 Matching to the String Theory Spectrum
14.7.3 N =85 Five-Dimensional Gauged Supergravity
14.7.4 Protected Correlation Functions and Anomalies
14.8 Correlation Functions
14.8.1 Two-Point Functions
14.8.2 Three-Point Functions
14.8.3 The Gravitational Action and the Conformal Anomaly
14.9 Wilson Loops
14.10 AdS5/CFT4 at Finite Temperature
14.10.1 N =44 Super Yang-Mills at Finite Temperature
14.10.2 The Near-Horizon Limit of Black D3-Branes
14.10.3 Finite Volume and Large-N Phase Transitions
14.10.4 Thermal Holographic Physics
14.10.5 Spatial Wilson Loops in (a Version of) QCD3
14.10.6 The Glueball Mass Spectrum
14.11 AdS4/CFT3 Correspondence
14.11.1 From M2 to D2
14.11.2 The Geometry of M2-Branes on R8/Zk
14.12 AdS7/CFT6 Correspondence
14.13 AdS3/CFT2 Correspondence
14.13.1 The Graybody Factors Revisited
Further Reading
Exercises
15. Applications of the Holographic Correspondence
15.1 Nonsupersymmetric YM from Five-Dimensional SYM
15.1.1 Extremal and Near-Extremal Dp-Branes in the Near-Horizon Limit
15.1.2 The Nonsupersymmetric D4-Brane Geometry
15.2 The Holographic Renormalization Group
15.2.1 Perturbations of CFT4
15.2.2 Domain Walls and Flow Equations
15.2.3 A Simple Setup
15.2.4 The Superpotential
15.2.5 General Properties of the Superpotential
15.2.6 Critical Points
15.2.7 Global Holographic RG Flows
15.2.8 Supersymmetric Flows in N=44 SYM
15.2.9 RG Flow Preserving N=14 Supersymmetry
15.3 Bottom-Up Holographic Theories for YM
15.3.1 Exploring Einstein-Dilaton Holography
15.3.2 The UV Asymptotics
15.3.3 The IR Asymptotics and Confinement
15.3.4 The "Glueball" Spectra
15.3.5 The Thermal Phase Diagram of Einstein-Dilaton Gravity
15.3.6 A Holographic Clone for Large-Nc YM
15.4 Holographic Flavor Dynamics
15.4.1 Flavor Branes
15.4.2 The D3-D7 Flavor System
15.4.3 The D4-D8-D8 Flavor System
15.4.4 Holography and Chiral Symmetry Breaking
15.4.5 Non-Abelian Flavor Dynamics
15.4.6 Chiral Symmetry Breaking and (Open-String) Tachyon Condensation
15.5 Nonequilibrium Thermal Physics
15.5.1 Linear Response in QFT
15.5.2 The Bulk/Boundary Correspondence in Real Time
15.5.3 Calculation of a Minkowski Retarded Correlator
15.5.4 Calculation of Retarded Correlators at Finite Temperature
15.5.5 The Holographic Calculation of the Shear Viscosity
15.5.6 The Fluid-Gravity Correspondence
15.6 Holography at Finite Density
15.6.1 Holographic CFTs at Finite Density
15.6.2 Emerging Criticality at Finite Density
15.6.3 Nonrelativistic Scaling Theories
15.6.4 Scaling and Hyperscaling Violation at Finite Density
15.7 Holographic Entanglement Entropy
15.7.1 Entanglement Entropy
15.7.2 The Ryu-Takayanagi Holographic Prescription
15.7.3 Holographic Entanglement Entropy at Finite Temperature
15.7.4 Phase Transitions and the Entanglement Entropy
15.8 The Randall-Sundrum Geometry
15.8.1 An Alternative to Compactification
Further Reading
Exercises
16. String Theory and Matrix Models
16.1 M(atrix) Theory
16.1.1 Membrane Quantization
16.1.2 Type-IIA D0-Branes and DLCQ
16.1.3 Gravitons and Branes in M(atrix) Theory
16.1.4 The Two-Graviton Interaction from M(atrix) Theory
16.2 Matrix Models and D=1 Bosonic String Theory
16.2.1 The Continuum Limit
16.2.2 Solving the Matrix Model
16.2.3 The Double-Scaling Limit
16.2.4 The Free-Fermion Picture
16.3 Matrix Description of D=2 String Theory
16.3.1 Matrix Quantum Mechanics and Free Fermions on the Line
16.3.2 The Continuum Limit
16.3.3 The Double-Scaling Limit
16.3.4 D-Particles, Tachyons, and Holography
Further Reading
Exercises
Appendixes
A. Two-Dimensional Complex Geometry
B. Differential Forms
C. Conformal Transformations and Curvature
C.1 Riemann and Weyl Tensors
C.2 Variations of Curvatures
C.3 The Curvature Bianchi Identities
C.4 Conformal Transformations
D. Theta and Other Elliptic Functions
D.1 ? and Related Functions
D.2 The Weierstrass Function
D.3 Modular Forms
D.4 Poisson Resummation
E. Toroidal Lattice Sums
F. Toroidal Kaluza-Klein Reduction
G. The Reissner-Nordström Black Hole
H. Electric-Magnetic Duality in D=4
I. Supersymmetric Actions in Ten and Eleven Dimensions
I.1 N =111 Supergravity
I.2 Type-IIA Supergravity
I.3 Type-IIB Supergravity
I.4 Type-II Supergravities: The Democratic Formulation
I.5 N =110 Supersymmetry
J. N =14, 24, Four-Dimensional Supergravity Coupled to Matter
J.1 N =14 Supergravity
J.2 N =24 Supergravity
K. BPS Multiplets in Four Dimensions
L. Geometry of Anti-de Sitter Space
L.1 The Minkowski Signature AdS
L.2 Euclidean AdS
L.3 The Conformal Structure of Flat Space
L.4 Fields in AdS
L.4.1 The Wave Equation in Poincaré Coordinates
L.4.2 The Bulk-Boundary Propagator
L.4.3 The Bulk-to-Bulk Propagator
L.4.4 Massless Gauge Fields in Poincaré Coordinates
Bibliography
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String Theory in a Nutshell

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