String Theory Demystified

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CHAPTER 14 Black Holes 253 Now, the area in fi ve dimensions is The entropy is g A rrr RV QQn 2 8 2 2 s s = 2π = 2π 1 2 3 1 5 S A = 4G5 (14.51) 5 5 6 2 8 where G = ( 2π) G RV = ( 2π) 8π g . Putting everything together we obtain 5 10 s s the result: S = 2π QQ 1 5n (14.52) One of the recent successes of string theory has been its ability to count up the microscopic states of a black hole to calculate its entropy. The result obtained in this manner agrees with the semiclassical expressions, providing strong support for string theory as a quantum theory of gravity. Quiz 1. Find the temperature of a D = 4 charged black hole. 2. The Hagedorn temperature is the temperature above which multiple strings would coalesce into a single string. Take the density of string states to be n= exp( 4πm α ′ ) and write down the partition function. What condition is necessary for the partition function to be fi nite? This gives the Hagedorn temperature. 3. Suppose that the sun were to collapse to a black hole. What would be its temperature? 4. Estimate the lifetime of a six solar mass black hole that is evaporating from the Hawking process. Summary
254 <strong>String</strong> <strong>Theory</strong> Demystifi ed 5. Consider a charged, rotating black hole in D = 5 dimensions with metric: 2 2 3⎛a 2 a 2 ⎞ ds =− dt − d + d 2 2 ⎝ ⎜ r r ⎠ ⎟ + − / 13 / 2 2 λ sin θ φ cos θ ψ λ dr + r dΩ 2 2 ( 3 ) πa J = 4G5 By calculating the area of the horizon, estimate the entropy. Take the charges to be the same as for the static charged black hole analyzed in the text.
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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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Page 218 and 219: CHAPTER 11 Type II String Theories
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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 250 and 251: CHAPTER 13 D-Branes 235 Tachyons ca
Page 252 and 253: CHAPTER 13 D-Branes 237 We consider
Page 254 and 255: CHAPTER 14 Black Holes Black holes,
Page 256 and 257: CHAPTER 14 Black Holes 241 This equ
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Page 260 and 261: CHAPTER 14 Black Holes 245 When the
Page 262 and 263: CHAPTER 14 Black Holes 247 hole squ
Page 264 and 265: CHAPTER 14 Black Holes 249 Entropy
Page 266 and 267: CHAPTER 14 Black Holes 251 Recallin
Page 270 and 271: CHAPTER 15 The Holographic Principl
Page 280 and 281: CHAPTER 16 String Theory and Cosmol
Page 294 and 295: Final Exam 1 1. Consider the lagran
Page 296 and 297: Final Exam 281 0 0 26. Find a simpl
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Page 300 and 301: Chapter 1 1. b 6. a 2. a 7. c 3. c
Page 302 and 303: Quiz Solutions 287 3. i( − ) 4.
Page 304 and 305: Quiz Solutions 289 Chapter 11 1. c
Page 306 and 307: 1. P 2. E µ 2 ν 1 ( X′ ) X µ
Page 308 and 309: Final Exam Solutions 293 27. Supers
Page 310 and 311: Final Exam Solutions 295 73. Types
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
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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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