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ISBN 10: 069112230X
ISBN 13: 978-0691122304
Author: Elias Kiritsis
String Theory in a Nutshell 1st Table of contents:
1 Introduction
1.1 Prehistory
1.2 The Case for String Theory
1.3 A Stringy Historical Perspective
1.4 Conventions
Bibliography
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
Bibliography
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 World-sheets
3.7 BRST Primer
3.8 BRST in String Theory and the Physical Spectrum
Bibliography
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 The Virasoro Algebra and the Central Charge
4.6 The 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 system
4.21 Orbifolds
4.22 CFT on Other Surfaces of Euler Number Zero
4.23 CFT on Higher-genus Riemann Surfaces
Bibliography
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
Bibliography
Exercises
6 Strings in Background Fields
6.1 The Nonlinear 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
Bibliography
Exercises
7 Superstrings and Supersymmetry
7.1 N = (1,1)2 World-sheet 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
7.6 One-loop Superstring Vacuum Amplitudes
7.6.1 The type-IIA/B superstring
7.6.2 The heterotic superstring
7.6.3 The type-I superstring
7.7 Closed Superstrings and T-duality
7.7.1 The type-II string theories
7.7.2 The heterotic string
7.8 Supersymmetric Effective Actions
7.9 Anomalies
Bibliography
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 Nonabelian Symmetry
8.7 T-duality and Orientifolds
8.8 D-branes as Supergravity Solitons
8.8.1 The supergravity solutions
8.8.2 Horizons and singularities
8.8.3 The extremal branes and their near-horizon geometry
8.9 NS5-branes
Bibliography
Exercises
9 Compactifications and Supersymmetry Breaking
9.1 Narain Compactifications
9.2 World-sheet versus Space-time Supersymmetry
9.2.1 N = 14 space-time supersymmetry
9.2.2 N = 24 space-time 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 the Type-II String
9.10 N = 26 Orbifolds of the Type-II String
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
Bibliography
Exercises
10 Loop Corrections to String Effective Couplings
10.1 Calculation of Heterotic Gauge Thresholds
10.2 On-shell Infrared Regularization
10.2.1 Evaluation of the threshold
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
Bibliography
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
Bibliography
Exercises
12 Black Holes and Entropy in String Theory
12.1 A Brief History
12.2 The Strategy
12.3 Black-hole Thermodynamics
12.3.1 The Euclidean continuation
12.3.2 Hawking evaporation and greybody factors
12.4 The Information Problem and the Holographic Hypothesis
12.5 Five-dimensional Extremal Charged Black Holes
12.6 Five-dimensional Nonextremal RN Black Holes
12.7 The Near-horizon Region
12.8 Semiclassical Derivation of the Hawking Rate
12.9 The Microscopic Realization
12.9.1 The world-volume theory of the bound state
12.9.2 The low-energy SCFT of the D1-D5 bound state
12.9.3 Microscopic calculation of the entropy
12.9.4 Microscopic derivation of Hawking evaporation rates
12.10 Epilogue
Bibliography
Exercises
13 The Bulk/Boundary Correspondence
13.1 Large-N Gauge Theories and String Theory
13.2 The Decoupling Principle
13.3 The Near-horizon Limit
13.4 Elements of the Correspondence
13.5 Bulk Fields and Boundary Operators
13.6 Holography
13.7 Testing the AdS5/CFT4 Correspondence
13.7.1 The chiral spectrum of N = 4 gauge theory
13.7.2 Matching to the string theory spectrum
13.7.3 N = 8 five-dimensional gauged supergravity
13.7.4 Protected correlation functions and anomalies
13.8 Correlation Functions
13.8.1 Two-point functions
13.8.2 Three-point functions
13.8.3 The gravitational action and the conformal anomaly
13.9 Wilson Loops
13.10 AdS5/CFT4 Correspondence at Finite Temperature
13.10.1 N = 4 super Yang-Mills theory at finite temperature
13.10.2 The near-horizon limit of black D3-branes
13.10.3 Finite-volume and large-N phase transitions
13.10.4 Thermal holographic physics
13.10.5 Spatial Wilson loops in (a version of) QCD3
13.10.6 The glueball mass spectrum
13.11 AdS3/CFT2 Correspondence
13.11.1 The greybody factors revisited
13.12 The Holographic Renormalization Group
13.12.1 Perturbations of the CFT4
13.12.2 Domain walls and flow equations
13.12.3 A RG flow preserving N = 1 supersymmetry
13.13 The Randall-Sundrum Geometry
13.13.1 An alternative to compactification
Bibliography
Exercises
14 String Theory and Matrix Models
14.1 M(atrix) Theory
14.1.1 Membrane quantization
14.1.2 Type-IIA D0-branes and DLCQ
14.1.3 Gravitons and branes in M(atrix) theory
14.1.4 The two-graviton interaction from M(atrix) theory
14.2 Matrix Models and D = 1 Bosonic String Theory
14.2.1 The continuum limit
14.2.2 Solving the matrix model
14.2.3 The double-scaling limit
14.2.4 The free-fermion picture
14.3 Matrix Description of D = 2 String Theory
14.3.1 Matrix quantum mechanics and free fermions on the line
14.3.2 The continuum limit
14.3.3 The double-scaling limit
14.3.4 D-particles, tachyons, and holography
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