String Theory Demystified

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CHAPTER 10 A Summary of Superstring Theory 191 supercharges has N = m supersymmetry. Finally, we can characterize each superstring theory by the gauge symmetry that it admits. All superstring theories eliminate the tachyon from the spectrum and include a graviton, so superstring theory naturally describes gravity. TYPE I SUPERSTRING THEORY Type I superstring theory can be characterized as follows: • It includes both open and closed strings. • It describes unoriented strings. • It has N = 1 supersymmetry. • It has SO(32) gauge symmetry. In addition, type I superstrings can have charges attached to their ends called Chan-Paton factors, a topic we will explore in a later chapter. TYPE II A Type II A theory describes closed, oriented superstrings. We can summarize the theory as follows: • It only includes closed strings. • It has N = 2 supersymmetry. • It has a U(1) gauge symmetry. Since this theory only has a U(1) gauge symmetry, it is not large enough to describe all the particle states seen in nature. It can describe gravity and electromagnetism, but cannot describe the weak or strong forces. The theory has 1 2 two supercharges, and Θ and Θ have opposite chirality. Practically speaking, this means that each fermion has a partner state with opposite chirality. TYPE II B Type II B theory also describes closed strings, also oriented. Although it includes fermionic states because it is a superstring theory, it has no gauge symmetry and so can only describe gravity. Like type II A theory, it has N = 2 supersymmetry, but 1 2 Θ and Θ have the same chirality. This remedies the diffi culty in type II A theory in that the fermions described in type II B theory do not have partners of opposite chirality. But the lack of a gauge group indicates the theory cannot be the whole story as far as a unifi ed theory of physics.
Dualities 192 String Theory Demystifi ed HETEROTIC SO(32) There are two heterotic theories that both describe closed, oriented strings. A heterotic theory is a kind of fusion between bosonic and superstring theory. The left movers and right movers are treated using different theories. We describe modes moving in one direction using bosonic string theory, and describe the modes moving in the opposite direction using N = 1 supersymmetry. The extra 16 dimensions of the bosonic theory are regarded as abstract, mathematical entities rather than actual space-time coordinates (like superspace). There are two heterotic theories, both with large gauge groups that can describe all particles in nature. The fi rst has SO(32). HETEROTIC E 8 × E 8 Similar to Heterotic SO(32) theory but has the gauge group E × E . 8 8 The state of string theory at this point appears to be a random mess, but the discovery of a set of dualities which relate the fi ve theories amongst themselves saved the day. The fact is that the fi ve theories are all related to one another, and we can transform between them. This has led physicists to believe that there exists an underlying theory. The fi ve superstring theories arise as different aspects or solutions of the underlying theory. While some aspects of the potentially underlying theory have been characterized, the actual underlying theory remains unknown. It goes by the name of M-theory. T-DUALITY We have already studied one duality in detail in Chap. 8, T-duality. To review Tduality relates a theory with a small compact dimension to a theory where that same dimension is large. T-duality relates string theories as follows: • It relates type II A and type II B theory. • It relates the two heterotic theories. T-duality can be summarized by saying that if we transform from a small to a large distance scale we exchange momentum and winding modes (and vice versa). T-duality relates type II A and type II B theory in that if we move from small to large distance in type II A theory, the theory is transformed into type II B theory and
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Accounting Demystified Advanced Cal
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Copyright © 2009 by The McGraw-Hil
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Contents vii BRST in String Theory-
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Contents ix CHAPTER 14 Black Holes
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PREFACE String theory is the greate
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Preface xiii time as this one to he
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CHAPTER 1 Introduction General rela
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CHAPTER 1 Introduction 13 Figure 1.
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CHAPTER 1 Introduction 15 • Type
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CHAPTER 1 Introduction 17 Close up,
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CHAPTER 1 Introduction 19 5. The mi
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CHAPTER 2 The Classical String I: E
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CHAPTER 2 Equations of Motion 23 To
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CHAPTER 2 Equations of Motion 25 No
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CHAPTER 2 Equations of Motion 29 ct
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CHAPTER 2 Equations of Motion 31 Th
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CHAPTER 2 Equations of Motion 33 is
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CHAPTER 2 Equations of Motion 35 Si
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CHAPTER 2 Equations of Motion 37 ho
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CHAPTER 2 Equations of Motion 39 Th
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CHAPTER 2 Equations of Motion 41 wh
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CHAPTER 2 Equations of Motion 43 In
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CHAPTER 2 Equations of Motion 47 We
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CHAPTER 2 Equations of Motion 49 In
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CHAPTER 3 The Classical String II:
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CHAPTER 3 Symmetries and Worldsheet
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CHAPTER 4 String Quantization At th
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CHAPTER 4 String Quantization Here,
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CHAPTER 4 String Quantization That
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CHAPTER 4 String Quantization Using
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CHAPTER 4 String Quantization expec
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CHAPTER 4 String Quantization † A
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CHAPTER 4 String Quantization To ob
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CHAPTER 4 String Quantization lower
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CHAPTER 4 String Quantization this)
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CHAPTER 4 String Quantization Norma
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CHAPTER 5 Conformal Field Theory Pa
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CHAPTER 6 BRST Quantization So far
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CHAPTER 6 BRST Quantization 117 It
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CHAPTER 6 BRST Quantization 119 Cal
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CHAPTER 6 BRST Quantization 121 The
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CHAPTER 6 BRST Quantization 123 To
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CHAPTER 6 BRST Quantization 125 The
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CHAPTER 7 RNS Superstrings The real
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CHAPTER 7 RNS Superstrings 129 EXAM
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CHAPTER 7 RNS Superstrings 131 SOLU
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CHAPTER 7 RNS Superstrings 133 In t
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CHAPTER 7 RNS Superstrings 135 Now,
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CHAPTER 7 RNS Superstrings 137 We c
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CHAPTER 7 RNS Superstrings 139 We o
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Page 168 and 169: CHAPTER 8 Compactifi cation and T-D
Page 182 and 183: CHAPTER 9 Superstring Theory Contin
Page 202 and 203: CHAPTER 10 A Summary of Superstring
Page 210 and 211: CHAPTER 11 Type II String Theories
Page 222 and 223: CHAPTER 12 Heterotic String Theory
Page 236 and 237: CHAPTER 13 D-Branes One of the most
Page 238 and 239: CHAPTER 13 D-Branes 223 The Space-T
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Page 254 and 255: CHAPTER 14 Black Holes Black holes,
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CHAPTER 14 Black Holes 241 This equ
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CHAPTER 14 Black Holes 243 Here, G
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CHAPTER 14 Black Holes 245 When the
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CHAPTER 14 Black Holes 247 hole squ
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CHAPTER 14 Black Holes 249 Entropy
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CHAPTER 14 Black Holes 251 Recallin
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CHAPTER 14 Black Holes 253 Now, the
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CHAPTER 15 The Holographic Principl
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CHAPTER 16 String Theory and Cosmol
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Final Exam 1 1. Consider the lagran
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Final Exam 281 0 0 26. Find a simpl
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Final Exam 283 68. When a single sp
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Chapter 1 1. b 6. a 2. a 7. c 3. c
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Quiz Solutions 287 3. i( − ) 4.
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Quiz Solutions 289 Chapter 11 1. c
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1. P 2. E µ 2 ν 1 ( X′ ) X µ
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Final Exam Solutions 293 27. Supers
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Final Exam Solutions 295 73. Types
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Books References Becker, K., M. Bec
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|NS〉 ⊕ |NS〉 Sector, 203 |NS
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INDEX 301 Cyclic model, 277 Cylinde
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INDEX 303 Mechanics, quantum. See Q
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INDEX 305 Schwarzschild metric, 242
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String Theory Demystified

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