String Theory Demystified

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CHAPTER 10 A Summary of Superstring Theory 193 vice versa (or switch momentum and winding modes). The same holds for the two heterotic theories. This means that type II A and type II B are really the same theory, and the two heterotic theories are really the same theory. S-DUALITY The second big duality that has been discovered is S-duality. Remember that a coupling constant determines the strength of an interaction, and in string theory the dilaton fi eld determines the value of the coupling constant. String theories have different coupling constants that are weak or strong. By letting ϕ →− ϕ where ϕ is the dilaton fi eld, since the coupling constant is defi ned from g = exp ϕ , we see that we can transform a large coupling constant into a small one and vice versa, changing a strong interaction into a weak one and vice versa. This is what S-duality is about. S-duality brings type I superstring theory into the fold. That is, under S-duality • Type I superstring theory is related to heterotic SO(32) superstring theory. • Type II B is S-dual to itself. So, a strong interaction in Type I superstring theory is the same as a weak interaction in heterotic SO(32) theory, and vice versa. In other words, the two theories are really the same theory at different coupling strengths. Quiz 1. T-duality relates string theories in which way? (a) It relates strong interactions in type II A theory to weak interactions in type II B theory. (b) It relates strong interactions in heterotic theory to weak interactions in type I theory. (c) It relates large and small distance scales and momentum and winding modes in two different theories. (d) It only relates large and small distance scales. 2. The most signifi cant difference between superstring theory and bosonic theory is (a) Bosonic theory has 16 extra space-time dimensions. (b) Superstring theory eliminates tachyon states and incorporates fermions into the theory.
194 String Theory Demystifi ed (c) Bosonic string theory eliminates tachyons. (d) Superstring theory has an unstable vacuum. 3. The difference between types II A and type II B theory is (a) Type II A theory is nonchiral and type II B theory is chiral. (b) Type II A theory only describes open strings. (c) Type II B theory only describes bosons. (d) Type II B theory is nonchiral and type II A theory is chiral. 4. The dilaton fi eld (a) Is only found in bosonic string theory. (b) Is related to the coupling constant, but only in heterotic theory. (c) Is related to the coupling constant in all string theories. (d) Is known to be a mathematical trick not found in nature. 5. Physicists were excited by dualities because (a) They add fermions to the theory. (b) They show that the fi ve superstring theories are related, so are different aspects of an underlying, unknown theory. (c) They show that bosonic and superstring theories are related, so are different aspects of an underlying, unknown theory. 6. The number of space-time dimensions in string theory (a) Is fi xed at 26 by an ad hoc assumption. (b) Is fi xed at 26 for superstring theories and 10 for bosonic string theory, because this eliminates ghost states from the theory. (c) Is fi xed at 10 for superstring theories and 26 for bosonic string theory, because this eliminates tachyon states from the theory. (d) Is fi xed at 10 for superstring theories and 26 for bosonic string theory, because this eliminates ghost states from the theory.
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Accounting Demystified Advanced Cal
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Copyright © 2009 by The McGraw-Hil
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For more information about this tit
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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 5 we say tha
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CHAPTER 1 Introduction 7 initial an
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CHAPTER 1 Introduction 9 a spin-2 b
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CHAPTER 1 Introduction 11 So if α
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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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CHAPTER 7 RNS Superstrings 141 OPEN
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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 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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