String Theory Demystified

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CHAPTER 10 A Summary of Superstring Theory 189 If a bosonic string theory has open strings, it automatically includes closed strings as well. This is due to the dynamical behavior of strings. If a string is open, it is possible for the endpoints to join together, forming a closed string state. Let’s summarize the four possibilities for bosonic string theory. If a bosonic string theory only includes closed strings that are oriented, then the spectrum of the theory includes the following states: • Tachyon • Massless antisymmetric tensor • Dilaton • Graviton Now, suppose that we only have closed strings, but the theory describes unoriented strings instead. That is, we can’t tell which direction we are moving along the string. In this case, the theory no longer includes a massless vector boson. We can summarize the key aspects of the spectrum as • Tachyon • Dilaton • Massless state which is the graviton Now let’s turn to bosonic string theories that include open as well as closed strings. Again, we can choose strings that are oriented and strings that are unoriented. The oriented theory is characterized by • Tachyon • Dilaton • Graviton • A massless antisymmetric tensor The closed string and open string tachyons are distinct. Choosing oriented open + closed bosonic string theory gives us • Tachyon • Dilaton • Massless graviton There is also a massless vector state for open strings, which can be oriented or unoriented. So we see that all bosonic string theories are plagued by the presence of a tachyon state. They have an unstable vacuum and do not include fermions. As a result, we are forced to consider superstring theories.
190 String Theory Demystifi ed Superstring Theory Superstring theory is a generalization of bosonic string theory which extends the theory to include fermions. There are fi ve different superstring theories. We use the word super in our description of them because all fi ve theories are based on a theory of physics known as supersymmetry. This theory is characterized by the idea that each fermion has a bosonic partner and vice versa. Some examples are given in Table 10.1. The existence of supersymmetry is a good indirect test of string theory. For string theory to be true, supersymmetry must exist in nature. At the time of writing no super-partner has ever been discovered, so supersymmetry either doesn’t exist in nature or it has been broken. One way it could be broken is that the superpartners are extremely massive. This means it would take high energies to see them. The Large Hadron Collider (LHC) set to begin operation in 2008 may be powerful enough to detect supersymmetry. So, superstring theory includes supersymmetry, which allows us to introduce fermions into the theory. It also includes ghost states, which are removed in an analogous, manner to what we saw in bosonic string theory. When the ghost states are removed we arrive at the second general characteristic of superstring theory: • There are 10 space-time dimensions. There are two ways to introduce supersymmetry into string theory, reviewed in Chaps. 7 and 9, respectively: • The RNS formalism adds supersymmetry to the worldsheet. • The GS formalism adds supersymmetry to space-time. We can still characterize superstring theories by noting whether or not they include open and/or closed strings, and whether those strings are oriented or unoriented. In addition, a superstring theory can be characterized by the number of supercharges used in the theory. This is done by saying that a theory with N = m Table 10.1 A listing of some particles and their postulated super-partners. Partner Superpartner Photon (spin 1) Photino (spin 1/2) Graviton (spin 2) Gravitino (spin 3/2) Quark (spin 1/2) Squark (spin 0) Electron (spin 1/2) Selectron (spin 0) Gluon (spin 0) Gluino (spin 1/2)
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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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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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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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