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E-raamat: Quarks and Leptons From Orbifolded Superstring

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  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Physics 954
  • Ilmumisaeg: 30-Oct-2020
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030540050
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Quarks and Leptons From Orbifolded SuperstringSuurem pilt
  • Formaat: EPUB+DRM
  • Sari: Lecture Notes in Physics 954
  • Ilmumisaeg: 30-Oct-2020
  • Kirjastus: Springer Nature Switzerland AG
  • Keel: eng
  • ISBN-13: 9783030540050
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This book is a guide for all those who want to explore the standard model using string theory. The approach pursued is halfway between a textbook and advanced research work and, accordingly, the book will allow both graduate students and particle phenomenologists to easily get acquainted with this fascinating field.

In this new edition the authors report on the status quo of the standard model following the discovery of the Higgs Boson, as well as the latest results concerning physics beyond the standard model. They present a formal introduction to string orbifolds and explain in detail how the massless states and the Kaluza-Klein spectra can be derived from the partition function. In turn, they provide an overview of orbifold phenomenology, by introducing the key aspects of string orbifolds in the context of SUSY standard models. In closing, the authors discuss the Grand Unified Theories (GUTs) from orbifolds and share key concepts regarding Calabi-Yau compactifications, M-theory and F-theory.
1 Introduction and Summary
1(14)
References
12(3)
2 Standard Model and Beyond
15(36)
2.1 The Standard Model
15(9)
2.2 Grand Unified Theories
24(7)
2.3 Supersymmetry
31(9)
2.3.1 Global Supersymmetry
31(3)
2.3.2 Local Supersymmetry, or Supergravity
34(4)
2.3.3 SUSY GUT
38(2)
2.4 Extra Dimensions
40(7)
2.4.1 Field Theory
40(1)
2.4.2 String Theory
41(4)
2.4.3 Compactification
45(2)
References
47(4)
3 Orbifold
51(28)
3.1 Orbifold Geometry
51(6)
3.1.1 Torus
52(2)
3.1.2 Toroidal Orbifold
54(1)
3.1.3 Fixed Points and Conjugacy Class
55(2)
3.2 One Dimensional Orbifolds
57(3)
3.2.1 S1/Za Orbifold
57(1)
3.2.2 Another Modding
58(1)
3.2.3 S1/(Z2 × Z'2) Orbifold
59(1)
3.3 Two Dimensional Orbifolds
60(6)
3.3.1 T2/Z2 Orbifold
60(2)
3.3.2 T2/Z3 Orbifold
62(1)
3.3.3 Geometry of Orbifold
63(1)
3.3.4 T2/Z6 Orbifold
64(2)
3.4 Classifying the Space Group
66(4)
3.4.1 Crystallography
66(1)
3.4.2 Finding Lattices for a Given Twist
67(1)
3.4.3 Coxeter Group
67(2)
3.4.4 Coxeter Lattice
69(1)
3.5 Six Dimensional Orbifold T6/ZN
70(8)
3.5.1 Supersymmetry Constraint
71(2)
3.5.2 T6/Z3 Orbifold
73(1)
3.5.3 Holonomy
74(1)
3.5.4 Homology, Number of Fixed Points
75(3)
References
78(1)
4 Spinors
79(14)
4.1 Spinors in General Dimensions
79(8)
4.1.1 Rotation and Vector
79(1)
4.1.2 Spinors in General Dimensions
80(7)
4.2 Supersymmetry Multiplets
87(4)
4.2.1 Five Dimensions
87(1)
4.2.2 Six Dimensions
88(3)
References
91(2)
5 Field Theoretic Orbifolds
93(36)
5.1 Fields on Orbifolds
93(15)
5.1.1 Scalar Fields
94(4)
5.1.2 Gauge Fields
98(4)
5.1.3 Fermions
102(4)
5.1.4 Graviton
106(2)
5.2 Realistic GUT Models
108(13)
5.2.1 SU(5) GUT in Five Dimension
108(5)
5.2.2 SO(10) GUT in Six Dimension
113(8)
5.3 Local Anomalies at Fixed Points
121(6)
References
127(2)
6 Quantization of Strings
129(54)
6.1 Bosonic String
129(16)
6.1.1 Action and Its Invariance Properties
130(6)
6.1.2 Conformal Symmetry and Virasoro Algebra
136(3)
6.1.3 Light-Cone Gauge
139(3)
6.1.4 Partition Function and Modular Invariance
142(3)
6.2 Superstring
145(15)
6.2.1 Worldsheet Action
146(4)
6.2.2 Light-Cone Gauge
150(3)
6.2.3 Spectrum and GSO Projection
153(6)
6.2.4 Superstring Theories
159(1)
6.3 Heterotic String
160(15)
6.3.1 Non-Abelian Gauge Symmetry
160(3)
6.3.2 Compactifying Several Dimensions
163(2)
6.3.3 Heterotic String
165(4)
6.3.4 Bosonization and Fermionization
169(6)
6.4 Open Strings
175(5)
6.4.1 Charged Open Strings
175(1)
6.4.2 Dirichlet Brane
176(2)
6.4.3 Type I String
178(1)
6.4.4 Duality of Strings
178(2)
References
180(3)
7 Strings on Orbifolds
183(32)
7.1 Twisted String
183(2)
7.2 Mode Expansion and Quantization
185(7)
7.2.1 Bosonic Left and Right Movers
185(3)
7.2.2 Fermionic Right Movers
188(2)
7.2.3 Shifting
190(2)
7.3 Embedding Gauge Group
192(5)
7.3.1 Associating Shift
192(2)
7.3.2 Modular Invariance
194(3)
7.4 The Standard Embedding
197(7)
7.4.1 Untwisted Sector
197(4)
7.4.2 Twisted Sector
201(2)
7.4.3 Need Improvement
203(1)
7.5 Wilson Lines
204(8)
7.5.1 Shifts Associated with Translations
204(3)
7.5.2 The Combination: Local Twists at the Fixed Points
207(1)
7.5.3 Projection Conditions in the Bulk
208(1)
7.5.4 Z3 Example
209(3)
References
212(3)
8 Formal Construction
215(22)
8.1 The String Hilbert Space
215(3)
8.1.1 Considering Modular Invariance
215(3)
8.2 Building Blocks of Partition Functions
218(9)
8.2.1 Bosonic String
218(7)
8.2.2 Current Algebra
225(2)
8.2.3 Right-Moving Fermions
227(1)
8.3 Heterotic String
227(9)
8.3.1 The Full Partition Function of Heterotic String
227(3)
8.3.2 Generalized GSO Projections
230(1)
8.3.3 Partition Function of the Z3 Orbifold
231(5)
References
236(1)
9 Non-prime Orbifolds
237(26)
9.1 The Geometry of Non-prime Orbifold
237(8)
9.1.1 T6/Z4 Orbifold
237(8)
9.2 Strings on Non-prime ZN Orbifolds
245(6)
9.2.1 Eigenstates of Point Group Element
245(2)
9.2.2 The Spectrum of T6/Z4 Orbifold Model
247(4)
9.3 Strings on ZN × ZM Orbifolds
251(4)
9.3.1 Combination of Twists
251(1)
9.3.2 Partition Function and Discrete Torsion
252(2)
9.3.3 Z3 × Z3 Example
254(1)
9.4 Wilson Lines on General Orbifolds
255(5)
9.4.1 Constraints on Wilson Lines
255(3)
9.4.2 Conjugacy Class
258(1)
9.4.3 Generalized GSO Projection
259(1)
References
260(3)
10 Interactions on Orbifolds
263(40)
10.1 Conformal Field Theory on Orbifolds
263(8)
10.1.1 Conformal Field Theory
264(3)
10.1.2 Vertex Operators for Interactions
267(4)
10.2 Selection Rules
271(6)
10.2.1 Space Group Invariance
272(3)
10.2.2 Lorentz Invariance
275(2)
10.3 Three-Point Correlation Function
277(6)
10.3.1 The Classical Part
278(5)
10.4 Four-Point Correlation Function
283(8)
10.4.1 The Classical Part
283(2)
10.4.2 The Quantum Part
285(3)
10.4.3 Factorization and Normalization
288(1)
10.4.4 Modular Property
289(2)
10.5 Phenomenology of Yukawa Couplings
291(10)
10.5.1 Couplings in Z3 Orbifold
291(4)
10.5.2 Yukawa Couplings in ZN Orbifolds
295(3)
10.5.3 Toward Realistic Yukawa Couplings
298(3)
References
301(2)
11 Effective Action
303(36)
11.1 Dimensional Reduction
304(5)
11.1.1 Dimeansional Reduction
304(5)
11.2 General Backgrounds
309(7)
11.2.1 Moduli Space
310(1)
11.2.2 Narain Compactification
311(2)
11.2.3 Moduli Fields
313(2)
11.2.4 Duality Between Two Heterotic String Theories
315(1)
11.3 Supersymmetric Action and Twisted Fields
316(15)
11.3.1 Kahler Potential
316(7)
11.3.2 Superpotential
323(1)
11.3.3 Gauge Kinetic Function
324(6)
11.3.4 No-scale Structure
330(1)
11.4 Shift Vector
331(1)
11.5 Anomaly Cancellation
331(5)
11.5.1 Anomaly Polynomial
332(2)
11.5.2 Elliptic Genus
334(2)
References
336(3)
12 Algebraic Structure
339(42)
12.1 Lie Algebra
339(8)
12.1.1 Lie Algebra
339(6)
12.1.2 Affine Lie Algebra
345(1)
12.1.3 Twisted Algebra
346(1)
12.2 Matter Fields
347(5)
12.2.1 Highest Weight Representations
347(1)
12.2.2 Integrability and No-adjoint Theorem
348(1)
12.2.3 Mass and Conformal Weight
349(3)
12.3 Automorphism
352(5)
12.3.1 Shift Vector
352(3)
12.3.2 Weyl Group
355(2)
12.4 General Action on Group Lattice
357(6)
12.4.1 Point Group Embedding
357(5)
12.4.2 Reducing the Rank by Orbifolding
362(1)
12.5 Asymmetric Orbifold
363(5)
12.5.1 Extending Group Lattice
363(2)
12.5.2 Symmetrizing Lattice
365(3)
12.6 Group Structure
368(10)
12.6.1 Classification of the Gauge Group
369(3)
12.6.2 Abelian Charge
372(3)
12.6.3 Complete Spectrum of SO(32) String
375(1)
12.6.4 Higher-Level Algebra
376(2)
References
378(3)
13 Orbifold Phenomenology
381(28)
13.1 Model Building
381(2)
13.2 String Unification
383(3)
13.2.1 Gauge Coupling Unification
383(1)
13.2.2 Standard-Like Models
384(2)
13.3 U(1) Charges
386(6)
13.3.1 Hypercharge
386(1)
13.3.2 Weak Mixing Angle
387(2)
13.3.3 Anomalous U(1)
389(3)
13.4 Three Families
392(3)
13.4.1 The Number of Fixed Points
392(1)
13.4.2 Number of Internal Dimensions
393(1)
13.4.3 Family Symmetry
394(1)
13.5 Discrete Symmetries
395(5)
13.5.1 Global and Discrete Symmetries
395(1)
13.5.2 R-Parity
396(1)
13.5.3 Violation
397(3)
13.6 "Invisible" Axion from String
400(3)
13.6.1 T Hooft Mechanism
400(1)
13.6.2 Domain Wall Number of "Invisible" Axion
401(1)
13.6.3 String Perspective
401(2)
13.7 Phenomenology on Electroweak
403(1)
13.8 The μ-Problem
404(1)
References
405(4)
14 String Unification
409(22)
14.1 Requirements for GUTs
409(1)
14.2 GUTs from Z12--1 Orbifold
410(19)
14.2.1 Without a Wilson Line
411(7)
14.2.2 A Model with a Wilson Line
418(7)
14.2.3 Doublet--Triplet Splitting
425(1)
14.2.4 U(1) Charges
426(1)
14.2.5 U(1)R Identification
426(1)
14.2.6 Discrete Symmetry Z4R
427(2)
14.2.7 A Z6 Orbifold Model
429(1)
14.2.8 Other Unified Models
429(1)
References
429(2)
15 Smooth Compactification
431(44)
15.1 Calabi--Yau Manifold
431(8)
15.1.1 Geometry Breaks Supersymmetry
432(1)
15.1.2 Complex Manifold
433(2)
15.1.3 Mode Expansion
435(4)
15.2 Standard Embedding
439(3)
15.2.1 Mode Expansion
439(2)
15.2.2 Number of Generations
441(1)
15.2.3 Wilson Lines
442(1)
15.3 General Embedding
442(8)
15.3.1 Background Gauge Field
443(1)
15.3.2 Spectrum
444(2)
15.3.3 Index Theorem
446(4)
15.4 Relation to Orbifold
450(2)
15.5 Algebraic Description
452(11)
15.5.1 A, D, E Singularity
453(1)
15.5.2 Resolution
453(3)
15.5.3 Classification
456(1)
15.5.4 Toric Geometry
457(6)
15.6 Dynamics of the Geometry
463(2)
15.7 Non-perturbative Vacua
465(8)
15.7.1 Instanton Background
466(3)
15.7.2 Non-perturbative String Vacua
469(4)
References
473(2)
16 Flavor Physics
475(24)
16.1 Data on Flavor Physics
478(4)
16.1.1 CKM Matrix
478(1)
16.1.2 Neutrino Oscillation and PMNS Matrix
479(3)
16.2 Theories on Flavor Physics in Field Theory
482(10)
16.2.1 Electroweak CP Violation
484(3)
16.2.2 B and L Generation
487(1)
16.2.3 Discrete Symmetries
488(3)
16.2.4 Continuous Symmetries
491(1)
16.3 Flavors from String Compactification
492(2)
16.4 CP Violation from String
494(1)
References
494(5)
17 Other Constructions
499(24)
17.1 Fermionic Construction
499(7)
17.1.1 Rules
500(2)
17.1.2 Models
502(4)
17.2 Intersecting Branes
506(5)
17.2.1 Models
510(1)
17.3 Magnetized Brane
511(3)
17.4 F-theory
514(7)
17.4.1 Models
518(3)
References
521(2)
A Useful Tables for Model Building 523(6)
Index 529
Kang-Sin Choi is assistant professor division chair of the Scranton Honors Program at Ewha Womans University, Seoul, Rep. of Korea. His research focuses on the Standard Model of particle physics and on how it can be completed by string theory.

Jihn E. Kim is professor emeritus at the Seoul National University, Rep. of Korea. As theoretical physicist, his research focuses on fundamental particles and their interactions, based on symmetry principles and superstring models. Some of his research interests concentrate on neutral currents, neutrino magnetic moment, invisible axion, dark matter, grand unification, and the cosmological constant problem.
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