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

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CHAPTER 6. SETTING 84Figure 6.5: D1-brane embeddings in trumpet (top-left: C = 0.1, mid-left: C = 1,bottom-left: C = 5) and cigar (top-right: C = 0.1, mid-right: C = 1, bottom-right:C = 5) geometries.
Chapter 7A First Example“Le temps n’apprécie rien qui se fait sans lui...”Lambic Brewery, BrusselsWritten on a piece <strong>of</strong> wood patientlyhanging in the fermentation chamber.As a way <strong>of</strong> getting acquainted with the problem at hand, a good place to start is toretrace the steps needed in order to obtain the results reported in [6]. In this article,a calculation is carried out in section 4 ressembling the one we will ultimately want tomake. The problem at hand is to find the spectrum <strong>of</strong> a D1-brane living on the cigartarget space using the small fluctuation <strong>DBI</strong> analysis. We will also perform the samecomputation for a D1-brane living on the trumpet, a case <strong>of</strong> interest since the D2-braneon the cigar we want to analyse came about by T-dualizing a D1-brane on the trumpet.As was mentioned earlier, we should be careful when interpreting the results <strong>of</strong> thiscomputation, since the exploding <strong>of</strong> the Φ field near the trumpet origin alerts us thatwe should also take into account extra perturbative terms. Nevertheless, despite this,going from the cigar to the trumpet is so easy, that this result will constitute a firstindication whether or not we are on the right track (<strong>of</strong> finding bound states, that is).In all the computations in this and the next chapter, we set α ′ = 1.7.1 D1-brane on the cigar7.1.1 Metric and actionThe cigar metric is given byds 2 = (dρ) 2 + (tanh ρ) 2 dτ 2 ; e −Φ = e −Φ 0chρ. (7.1)85
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Master ThesisDBI <
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ContentsAcknowledgements 1Samenvatt
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7.1.4 Perturbed equations o
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SamenvattingDe zogehete snaartheori
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Chapter 1Introduction“Smokey, my
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CHAPTER 1. INTRODUCTION 6sight seem
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Chapter 2Bosonic String</st
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CHAPTER 2. BOSONIC STRINGS 14moment
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CHAPTER 2. BOSONIC STRINGS 162.3 Eq
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CHAPTER 2. BOSONIC STRINGS 18we see
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CHAPTER 2. BOSONIC STRINGS 20which
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CHAPTER 2. BOSONIC STRINGS 22which
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CHAPTER 2. BOSONIC STRINGS 24from w
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CHAPTER 2. BOSONIC STRINGS 26to use
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CHAPTER 2. BOSONIC STRINGS 28This a
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CHAPTER 2. BOSONIC STRINGS 30World
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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
Page 50 and 51: CHAPTER 3. SUPERSTRINGS 423.3.1 Clo
Page 52 and 53: CHAPTER 3. SUPERSTRINGS 443.4 Quant
Page 54 and 55: CHAPTER 3. SUPERSTRINGS 46freedom t
Page 56 and 57: CHAPTER 3. SUPERSTRINGS 48hence, fe
Page 58 and 59: CHAPTER 3. SUPERSTRINGS 50miraculou
Page 60 and 61: CHAPTER 3. SUPERSTRINGS 52associate
Page 62 and 63: CHAPTER 4. CONFORMAL INVARIANCE 54t
Page 64 and 65: CHAPTER 4. CONFORMAL INVARIANCE 56w
Page 66 and 67: CHAPTER 4. CONFORMAL INVARIANCE 58i
Page 68 and 69: Chapter 5Branes“Many speak <stron
Page 70 and 71: CHAPTER 5. BRANES 62but if the stri
Page 72 and 73: CHAPTER 5. BRANES 64meaning that th
Page 74 and 75: CHAPTER 5. BRANES 66i.e. our origin
Page 76 and 77: CHAPTER 5. BRANES 68The presence <s
Page 78 and 79: CHAPTER 5. BRANES 70heuristic argum
Page 80 and 81: CHAPTER 5. BRANES 72where F 12 is t
Page 83 and 84: Part IIIResearch75
Page 85 and 86: CHAPTER 6. SETTING 77it does. This
Page 87 and 88: CHAPTER 6. SETTING 79of</st
Page 89 and 90: CHAPTER 6. SETTING 81It was mention
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Page 95 and 96: CHAPTER 7. A FIRST EXAMPLE 877.1.3
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Page 103 and 104: CHAPTER 7. A FIRST EXAMPLE 95This t
Page 105 and 106: CHAPTER 8. COMPUTATIONS 97and the i
Page 107 and 108: CHAPTER 8. COMPUTATIONS 998.4 Regul
Page 109 and 110: CHAPTER 8. COMPUTATIONS 1018.5 Equa
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Page 113: Chapter 9Conclusion & Final Thought
Page 116 and 117: BIBLIOGRAPHY 108[16] Polchinski J.,
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DBI Analysis of Open String Bound States on Non-compact D-branes

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