String Theory Demystified

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CHAPTER 12 Heterotic String Theory 219 This can only be true if the canonical momentum has an expansion of the form I i p a e 16 I = ∑ i R 2 i= 1 where the a i are integer coeffi cients of the expansion. This has the same form obtained in the one-dimensional case, where we found p = n/R. So, to compactify over a lattice you defi ne basis vectors, then sum up over all directions dividing by the radius in each direction. In this chapter, we gave an overview of the heterotic string. Using the usual approach to supersymmetry, we wrote down the action, applied anticommutation relations, defined number operators, and applied the mass-shell condition. As a result, we found a theory which contains the dilaton and graviton and their superpartners among the massless states. Further analysis would show that the theory is large enough to include the standard model. We can summarize this as follows: • The heterotic theory has left-moving and right-moving currents on the string. • The right-moving currents carry supersymmetry charges and give fermionic states. • The left-moving currents carry the conserved charges of Yang-Mills theories. After describing the basic machinery of the heterotic string, we illustrated how compactifi cation can be used to get rid of the unwanted 16 extra dimensions that are added to the theory by including the left-moving bosonic theory. Quiz j 1. How many states are there for the left-moving sector of the form α −1 0 I 2. How many states in the left-moving states have the form α −1 0 ? i Summary ?
220 String Theory Demystifi ed 3. Consider the constraint equations in the compactifi cation section. Why is I ( ∂ −∂ ) X = 0 the only constraint on the bosonic modes for the extra 16 τ σ dimensions? 4. Given the action 16 1 2 ⎛ i a I a − ⎞ S =− d ∂ X ∂ X + ∂ X ∂ X + iS ∂ +∂ S a i a I 4πα ′ ∫ σ ∑ Γ ( ) τ σ ⎝ ⎜ ⎠ ⎟ , what are the I= i commutation relations satisfi ed by the bosonic modes? 5. Consider the description of the heterotic string in the compactifi cation section and calculate ( 1+ Γ ) S = 0 a . 11
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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
Page 184 and 185: 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
Page 240 and 241: CHAPTER 13 D-Branes 225 Once again
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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 264 and 265: CHAPTER 14 Black Holes 249 Entropy
Page 266 and 267: CHAPTER 14 Black Holes 251 Recallin
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Page 270 and 271: CHAPTER 15 The Holographic Principl
Page 280 and 281: CHAPTER 16 String Theory and Cosmol
Page 282 and 283: CHAPTER 16 String Theory and Cosmol
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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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