String Theory in a Nutshell: Second Edition

Elias Kiritsis

The essential introduction to modern string theory—now fully expanded and revised

In a Nutshell

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Published:: Apr 16, 2019
Copyright:: 2019
Main_subject:: Physics & Astronomy

ebook

Sale Price:: $73.50/£61.60
Price:: ~~$105.00~~/~~£88.00~~
ISBN:
Published:: Apr 16, 2019
Copyright:: 2019
Main_subject:: Physics & Astronomy

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String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world’s leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature.

This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly.

The essential one-volume reference for students and researchers in theoretical high-energy physics
Now fully expanded and revised
Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy
Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems
An online illustration package is available to professors

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 σ-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 ϑ 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
Index

Praise for the previous edition:“What sets this book apart from other recent and older texts on string theory is that, while providing the level of detail in the derivation of all central results that is necessary for an introductory textbook, Kiritsis maintains a brisk and steady pace, and also includes a colloquial discussion of new concepts at the beginning of every section.”—Johannes Walcher, Mathematical Reviews

“This textbook on string theory presents the state of the art of this quickly developing topic.”—Hans-Jürgen Schmidt, Zentralblatt MATH

“An excellent reference for any graduate student interested in string theory. Kiritsis succinctly describes many of the recent developments that are necessary background to current research.”—Juan Maldacena, Institute for Advanced Study

“There is a definite need for a short, speedy introduction to modern string theory. Kiritsis beautifully fills this gap—including all essential areas, but remaining relatively concise, so that a beginning student can work through the entire text.”—Andrew Strominger, Harvard University

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