String Theory Demystified

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Final Exam Solutions 295 73. Types II A and II B, and the two heterotic theories. 74. You can tell direction along the string. 75. m 2 =− 1 / α ′ 76. It contains open and closed strings, all other superstring theories describe closed strings. 77. There are two theories, one with E8 × E8 and one with SO(32). 78. The universe expands in n directions but contracts in D-n directions as time increases. 79. It makes contracting and expanding solutions dual to one another. 80. It defi nes a minimum radius such that Rmin = α ′ . 81. There are two 3-branes separated along a fourth spatial dimension. 82. β φ → 0 83. The number of space-time dimensions is 26. 84. It is equivalent to Einstein’s equation for a scalar fi eld. 85. Extreme black holes in string theory can have magnetic charge as well. 86. In a theory with R′ = α ′ / R, the state is transformed to ( nK. , ) 87. They are unchanged. 88. The state has the same mass m in the dual theory. 89. ∂ + X =∂+ ∂ 25 X25 −X25 =−∂−X25 90. It vanishes. 91. The winding numbers are fractional. 92. Neumann 93. p = 02468 , , , , 94. Dirichlet 1 ⎛ T 95. S = ⎞ g ⎝ 2π ⎠ 1 96. E = T = 2πα ′ φ 1 97. e = s g s 5 ∫ 10 d x 1− ( E T) 2
296 <strong>String</strong> <strong>Theory</strong> Demystifi ed 25 25 98. Constant terms x = p = 0, sum over modes goes to sum over half- µ µ µ µ α α α α n n+ 12 / n n+ 12 / integral modes, that is, → , → . n n+ 1/ 2 n n+ 1/ 2 99. H pp N N p p D i i ∞ 1 = + ⎡ − + − + ⎤ + + ∑ 3 1 2 α ′ ⎣⎢ 12 24 ⎦⎥ n= 1 2 ⎛ 15 100. α ′ m = 4 N − ⎞ ⎝ 16⎠
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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 3 fl at spac
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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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CHAPTER 7 RNS Superstrings 143 If w
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CHAPTER 7 RNS Superstrings 145 The
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CHAPTER 7 RNS Superstrings 147 From
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CHAPTER 7 RNS Superstrings 149 The
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CHAPTER 7 RNS Superstrings 151 3. A
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CHAPTER 8 Compactifi cation and T-D
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CHAPTER 9 Superstring Theory Contin
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CHAPTER 10 A Summary of Superstring
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CHAPTER 11 Type II String Theories
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CHAPTER 12 Heterotic String Theory
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CHAPTER 13 D-Branes One of the most
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CHAPTER 13 D-Branes 223 The Space-T
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CHAPTER 13 D-Branes 225 Once again
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CHAPTER 13 D-Branes 227 and ( X i i
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CHAPTER 13 D-Branes 229 fi rst exci
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CHAPTER 13 D-Branes 231 a set of D-
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CHAPTER 13 D-Branes 233 D-brane 1 a
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CHAPTER 13 D-Branes 235 Tachyons ca
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CHAPTER 13 D-Branes 237 We consider
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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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Page 294 and 295: Final Exam 1 1. Consider the lagran
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Page 304 and 305: Quiz Solutions 289 Chapter 11 1. c
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Page 312 and 313: Books References Becker, K., M. Bec
Page 314 and 315: |NS〉 ⊕ |NS〉 Sector, 203 |NS
Page 316 and 317: INDEX 301 Cyclic model, 277 Cylinde
Page 318 and 319: INDEX 303 Mechanics, quantum. See Q
Page 320 and 321: INDEX 305 Schwarzschild metric, 242
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