String Theory Demystified

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CHAPTER 13 D-Branes One of the most interesting developments in string theory over the last decade or so was the realization that the theory could incorporate higher-dimensional extended objects—that is, objects beyond one-dimensional strings. When these objects are associated with Dirichlet boundary conditions we call these extended objects Dp-branes, where p indicates the number of spatial dimensions it has. The word “brane” comes about by analogy. In our everyday world of three spatial dimensions, we are familiar with the notion of a membrane, which is a two-dimensional surface that can separate two regions. The idea of a Dp-brane is to generalize this concept to consider an extended object of p dimensions. If the number of spatial dimensions of the D-brane is equal to the total number of spatial dimensions in the entire space-time, we say that we have a space-fi lling brane. There are three pertinent examples we can think of immediately to illustrate space-fi lling branes: • If space-time is just the three spatial dimensions and one time dimension we are used to from everyday life and special/general relativity, then a D3-brane would be a space-fi lling brane. Copyright © 2009 by The McGraw-Hill Companies, Inc. Click here for terms of use.
222 <strong>String</strong> <strong>Theory</strong> Demystifi ed • In bosonic string theory, there are 26 space-time dimensions. So, a D25-brane would be a space-filling brane. • In superstring theory, there are 10 space-time dimensions. So, a spacefi lling brane has 9 spatial dimensions and is called a D9-brane. Chances are if you’re reading this book you’ve completed calculus so you’re familiar with the notion of a hyperplane. When fi rst getting started, the best way to think about a D-brane is • It is a hyperplane-like object. • The endpoints of open strings are attached to it. This is illustrated in Fig. 13.1. Note, however, that not all D-branes are hyperplanes, but this is a good way to visualize them. The spatial dimensions not associated with the brane are called the bulk. The volume of the brane is called the world-volume. Note that time fl ows everywhere, in the bulk and on the D-brane as well. A model of our universe has been proposed where we live in a D3-brane and the bulk consists of the remaining extra spatial dimensions. Perhaps the most fundamental physical insight that has resulted from the study of D-branes is that • The interactions of the standard model (electromagnetism, strong, and weak forces) are constrained to the brane. • Gravity can escape from the brane. Gravitational forces are distributed in the brane and also throughout the higher dimensions. Hence, the strength of gravity is diluted by the higher dimensions. This explains why its strength is so different from that of the other known forces. For simplicity, we will discuss branes within the context of bosonic string theory. D-brane Open string with ends attached to D-brane Space-time outside D-brane is the “bulk’’ Figure 13.1 A D-brane is a hyperplane-like object to which open strings attach.
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Copyright © 2009 by The McGraw-Hil
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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 9 a spin-2 b
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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 9 Superstring Theory Contin
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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 238 and 239: CHAPTER 13 D-Branes 223 The Space-T
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Page 254 and 255: CHAPTER 14 Black Holes Black holes,
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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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