String Theory Demystified

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CHAPTER 1 Introduction 13 Figure 1.5 Fundamental particles are extended one-dimensional objects called strings. Figure 1.6 A closed string has no loose ends. Strings can be open (Fig. 1.5) or closed (Fig. 1.6), the latter meaning that the ends are connected. Excitations of the string give different fundamental particles. As a particle moves through space-time, it traces out a world line. As a string moves through spacetime, it traces out a worldsheet (see Fig. 1.7), which is a surface in space-time parameterized by ( σ, τ ) . A mapping x µ ( τ, σ)maps a worldsheet coordinate ( σ, τ) to the space-time coordinate x. So, in the world according to string theory, the fundamental objects are tiny strings with a length on the order of the Planck scale (10 33 − cm). Like any string, t Schematic representation of a string moving through spacetime, it is represented by a worldsheet (a tube for a closed string) x t A particle moving through space-time has a world line Figure 1.7 A comparison of a worldsheet for a closed string and a world line for a point particle. The space-time coordinates of the world line are parameterized as µ µ x = x () τ , while the space-time coordinates of the worldsheet are parameterized as x µ (, τ σ ) where ( σ, τ) give the coordinates on the surface of the worldsheet. x
14 String Theory Demystifi ed these fundamental strings can vibrate and vibrations at different resonant frequencies (excitations of the string) give rise to particles with different properties. For a particle with spin J and mass mJ , the mass and spin of the particle are related to the string tension through α ′ as J = α ′ mJ 2 (1.17) Think of a vibrating string having different modes in the way that a violin string can vibrate at different frequencies. Instead of having a plethora of “fundamental particles” with mysterious origin, there is only one fundamental object—a string that vibrates with different modes giving the appearance that there are multiple fundamental objects. Each mode appears as a different particle, so one mode could be an electron, while another, different mode could be a quark. It is possible for strings to split apart and to combine. Let’s focus on strings splitting apart. Suppose that a parent string is vibrating in a mode corresponding to particle A. It splits in two, with resulting daughter strings vibrating in modes corresponding to particles B and C respectively. This process of splitting corresponds to the particle decay: A→ B+ C Conversely, strings can join up as well, combining to form a single string. This is a process that until now we have thought of as particle absorption. So processes that seemed more on the mysterious side, such as particle decay, are explained with a simple conceptual framework. TYPES OF STRING THEORIES There appear to be fi ve different types of string theory, but it has been shown that they are different ways of looking at the same theory, with the different types related by dualities. The fi ve basic types are • Bosonic string theory This is a formulation of string theory that only has bosons. There is no supersymmetry, and since there are no fermions in the theory it cannot describe matter. So it is really just a toy theory. It includes both open and closed strings and it requires 26 space-time dimensions for consistency. • Type I string theory This version of string theory includes both bosons and fermions. Particle interactions include supersymmetry and a gauge group SO( 32 ) .This theory and all that follow require 10 space-time dimensions for consistency.
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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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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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