DBI Analysis of Open String Bound States on Non-compact D-branes

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Chapter 1Introduction“Smokey, my friend, you’re entering a world <strong>of</strong> pain. Aworld <strong>of</strong> pain...”Coen BrothersThe Big Lebowski<strong>String</strong> theory is a field that is still in full blossoming, despite the fact that it has actuallybeen around for about four decades. It took its first steps rather slowly and faced a hardtime getting generally accepted for several reasons. In this introductory chapter, a bit<strong>of</strong> ink will be spilled in order to paint with very broad strokes the general idea <strong>of</strong> whatstring theory is all about, and in trying to retrace some <strong>of</strong> the most important steps itwent through from its inception until now.1.1 <strong>String</strong> theory in a nutshellUnlike the reference work <strong>of</strong> the same name [13], this nutshell will not comprise severalhundreds <strong>of</strong> pages and will, hopefully, be accessible to everyone.<strong>String</strong> theory sometimes seems like a giant box full <strong>of</strong> different types <strong>of</strong> buildingblocks. These building blocks allow one to construct entire worlds, and the name <strong>of</strong> thegame is <strong>of</strong> course to build a world that looks remarkably close to ours. However, due toan as <strong>of</strong> yet insufficient understanding <strong>of</strong> the fundamental behaviour <strong>of</strong> these buildingblocks, this task proves itself excruciatingly difficult.The Standard Model allowed for the unification <strong>of</strong> three <strong>of</strong> the four fundamentalforces at a quantum (field) level; electro-magnetism, and the weak and strong nuclearforces. Its success has been confirmed time and again by the tear inducingly beautifulagreement <strong>of</strong> its predicitions with experimental results. Which made its predictive powerall the more puzzling, given that the theory exhibited some undeniable shortcomings.For one, it relied on a great number <strong>of</strong> parameters (couplings, masses,...) which neededto be tuned by hand in order to agree with Nature. Furthermore, it did not incorporatethe fourth fundamental force: gravity. And last but certainly not least, the high energy4
CHAPTER 1. INTRODUCTION 5behaviour <strong>of</strong> the theory seemed to be far for from ideal, a regime at which gravity canno longer be ignored.All these problems suggested that a new, or at least improved, theory should exist,one that is more fundamental than the Standard Model. As far as the improvement<strong>of</strong> the Standard Model is concerned, two major developments occured. The first one isthe construction <strong>of</strong> the so-called Grand Unified Theories, which try to extend the gaugegroups <strong>of</strong> the Standard Model in order to further unify the theory. The other one issupersymmetry. But still, this proves to be insufficient.So rather than extending the SM, one could also envisage the second approach: tocreate a new fundamental theory.Figure 1.1: Taken from [23].<strong>String</strong> theory is a quantum theory that has the potential to incorporate all fourfundamental forces <strong>of</strong> Nature. Its novelty lies in the fact that it radically alters the concept<strong>of</strong> what an elementary particle is. All other theories except string theory considerelementary particles as being point particles; particles without any physical dimension.<strong>String</strong> theory raises the possibility that the fundamental constituents <strong>of</strong> matter mightwell have a physical dimension. It started out looking at fundamental constituentswhich extend in one spatial dimension closely resembling strings, explaining its name.The idea is that these strings can oscillate, and that different oscillations give rise todifferent particles. However, the original string soon became a “superstring,” and othermulti-dimensional objects also naturally appeared to inhabit the theory. Despite allthis, the name “string theory” remained; it simply gained weight.Complementing the possibility that it might be a quantum theory <strong>of</strong> gravity, stringtheory exhibits a number <strong>of</strong> other features that sets it apart from other theories. Forone, it contains only one dimensionfull parameter, namely the string length l s , the length<strong>of</strong> the fundamental constituent. All other “parameters” are dictated by the theory. Asa specific example, string theory demands the number <strong>of</strong> space-time dimensions to be10 (in superstring theory) in order to be consistent. It is the first theory to imposethe dimensionality <strong>of</strong> the space-time it lives in. Admittedly, 10 dimensions at first
Page 1: Master ThesisDBI <
Page 5 and 6: ContentsAcknowledgements 1Samenvatt
Page 7: 7.1.4 Perturbed equations o
Page 10 and 11: SamenvattingDe zogehete snaartheori
Page 14: CHAPTER 1. INTRODUCTION 6sight seem
Page 20 and 21: Chapter 2Bosonic String</st
Page 22 and 23: CHAPTER 2. BOSONIC STRINGS 14moment
Page 24 and 25: CHAPTER 2. BOSONIC STRINGS 162.3 Eq
Page 26 and 27: CHAPTER 2. BOSONIC STRINGS 18we see
Page 28 and 29: CHAPTER 2. BOSONIC STRINGS 20which
Page 30 and 31: CHAPTER 2. BOSONIC STRINGS 22which
Page 32 and 33: CHAPTER 2. BOSONIC STRINGS 24from w
Page 34 and 35: CHAPTER 2. BOSONIC STRINGS 26to use
Page 36 and 37: CHAPTER 2. BOSONIC STRINGS 28This a
Page 38 and 39: CHAPTER 2. BOSONIC STRINGS 30World
Page 40 and 41: CHAPTER 2. BOSONIC STRINGS 32This g
Page 42 and 43: CHAPTER 2. BOSONIC STRINGS 34<stron
Page 44 and 45: CHAPTER 2. BOSONIC STRINGS 36For th
Page 46 and 47: Chapter 3Superstrings“One <strong
Page 48 and 49: CHAPTER 3. SUPERSTRINGS 40In D dime
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Page 54 and 55: CHAPTER 3. SUPERSTRINGS 46freedom t
Page 56 and 57: CHAPTER 3. SUPERSTRINGS 48hence, fe
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CHAPTER 4. CONFORMAL INVARIANCE 54t
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CHAPTER 4. CONFORMAL INVARIANCE 56w
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CHAPTER 4. CONFORMAL INVARIANCE 58i
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Chapter 5Branes“Many speak <stron
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CHAPTER 5. BRANES 62but if the stri
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CHAPTER 5. BRANES 64meaning that th
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CHAPTER 5. BRANES 66i.e. our origin
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CHAPTER 5. BRANES 68The presence <s
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CHAPTER 5. BRANES 70heuristic argum
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CHAPTER 5. BRANES 72where F 12 is t
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Part IIIResearch75
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CHAPTER 6. SETTING 77it does. This
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CHAPTER 6. SETTING 79of</st
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CHAPTER 6. SETTING 81It was mention
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CHAPTER 6. SETTING 83through the in
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Chapter 7A First Example“Le temps
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CHAPTER 7. A FIRST EXAMPLE 877.1.3
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CHAPTER 7. A FIRST EXAMPLE 91with
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CHAPTER 7. A FIRST EXAMPLE 95This t
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CHAPTER 8. COMPUTATIONS 97and the i
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CHAPTER 8. COMPUTATIONS 998.4 Regul
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CHAPTER 8. COMPUTATIONS 1018.5 Equa
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CHAPTER 8. COMPUTATIONS 103which de
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Chapter 9Conclusion & Final Thought
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BIBLIOGRAPHY 108[16] Polchinski J.,
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⌈I’m so glad you cameI’m so g
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DBI Analysis of Open String Bound States on Non-compact D-branes

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