Standard Model from Intersecting Branes?

In summary: The low-energy part of the spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3 The high-energy part of the spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344 On the consistency of the low-energy part of the spectrum . . . . . . . . . . . . . . . . . . . . . 375 Summary . . . . . . . . . . . . . . . . . . . . . . .
  • #1
selfAdjoint
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This is currently a hot topic, and I hope to get some discussion of it from our resident experts on stringy subjects. To start off here's a recent paper, maybe not the greatest but typical and fairly wide-ranging. If you know a better one, or a turorial on the subject why not favor us with a link!

http://arxiv.org/abs/hep-th/0307252
 
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  • #2
Originally posted by selfAdjoint
This is currently a hot topic, and I hope to get some discussion of it from our resident experts on stringy subjects. To start off here's a recent paper, maybe not the greatest but typical and fairly wide-ranging. If you know a better one, or a turorial on the subject why not favor us with a link!

http://arxiv.org/abs/hep-th/0307252

I'm sorry but my computer has severe problems downloading sites that use different formats of text. Could you perhaps explain the gist of the site?
 
  • #3
whoa! i know that guy, his office is right next to mine! i would like to understand his thesis, but so far i have not been able.

let s give it a try. if anyone wants me to ask fernando some questions, i can do that.
 
  • #4
Originally posted by lethe
whoa! i know that guy, his office is right next to mine! i would like to understand his thesis, but so far i have not been able.

let s give it a try. if anyone wants me to ask fernando some questions, i can do that.

Lethe, I have the impression that Fernando Marchesano is at the University of Madrid so that, if you were to step next door to his office to ask him a question, you would perhaps by magic (or by my mistaken impression) be in Spain
 
  • #5
Originally posted by marcus
Lethe, I have the impression that Fernando Marchesano is at the University of Madrid so that, if you were to step next door to his office to ask him a question, you would perhaps by magic (or by my mistaken impression) be in Spain

fernando got his PhD from the university of madrid, i believe. he is a postdoc at my university.
 
  • #6
Originally posted by lethe
fernando got his PhD from the university of madrid, i believe. he is a postdoc at my university.

i checked the seminar schedule. it seems he is doing the string seminar next week. i think i will attend.
 
  • #7
Super! Maybe you can bring us some news?
 
  • #8
Originally posted by selfAdjoint
This is currently a hot topic, and I hope to get some discussion of it from our resident experts on stringy subjects. To start off here's a recent paper, maybe not the greatest but typical and fairly wide-ranging. If you know a better one, or a turorial on the subject why not favor us with a link!

http://arxiv.org/abs/hep-th/0307252

Well here is the table of contents.

1 Introduction 1
1.1 The quest for the Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Dualities and D-branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Intersecting brane worlds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Branes intersecting at angles 11
2.1 Flat intersecting D-branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 T-dual picture: D-branes with magnetic fluxes . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Toroidal and orbifold compactifications . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Orientifold compactifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5 General intersecting D-branes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3 E ective theory spectrum 27
3.1 Closed string spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1 Toroidal case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.2 Orbifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.1.3 Orientifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Open string spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.1 Toroidal case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2.2 Orbifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.3 Orientifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.3 Intermediate spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.1 DaDa sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3.2 DaDb sector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.3 Extra massless states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4 RR tadpoles and anomalies 45
4.1 Tadpoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1.1 Toroidal case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.2 Orbifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
i
ii CONTENTS
4.1.3 Orientifold case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2 Anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.1 Cubic non-Abelian anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2.2 Mixed and cubic U(1) anomalies . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.3 Massive U(1)’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5 Looking for the Standard Model 65
5.1 The Standard Model intersection numbers . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 D6-brane models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 Massive U(1)’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2.2 Absence of tachyons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2.3 The Higgs sector and electroweak symmetry breaking . . . . . . . . . . . . . . 74
5.2.4 Yukawas and gauge coupling constants . . . . . . . . . . . . . . . . . . . . . . . 77
5.3 D5-brane models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.3.1 D5 Standard Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3.2 D5 Left-Right Symmetric Models . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.3.3 Some extra D5-brane SM models . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.3.4 Low-energy spectrum beyond the SM . . . . . . . . . . . . . . . . . . . . . . . 91
5.3.5 Lowering the string scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.4 D4-brane models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Supersymmetry and calibrations 97
6.1 Supersymmetries on T 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 Calabi-Yau and Special Lagrangian geometry . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.1 The six-torus revisited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.2 Orientifolded geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.3 Some applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.4 An MSSM-like example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
7 Yukawa couplings 111
7.1 Intersecting brane models and Yukawa couplings . . . . . . . . . . . . . . . . . . . . . 112
7.1.1 The role of worldsheet instantons . . . . . . . . . . . . . . . . . . . . . . . . . . 112
7.1.2 Yukawa couplings in intersecting D-brane models . . . . . . . . . . . . . . . . . 114
7.2 The general form of Yukawa couplings in toroidal models . . . . . . . . . . . . . . . . 117
7.2.1 Computing Yukawas on a T 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
7.2.2 Higher dimensional tori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.2.3 Physical interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7.3 Yukawa couplings in the MSSM-like example . . . . . . . . . . . . . . . . . . . . . . . 127
7.4 Extension to elliptic fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
CONTENTS iii
7.5 Yukawa versus Fukaya . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
8 Conclusions 137
A Q-basis formalism 141
A.1 General properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
A.2 D6-branes on T 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
A.3 D5-branes on T 4 × C/ZN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
A.4 D4-branes on T 2 × C2/ZN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
B K-theory constraints 147
C Higher dimensional holomorphic discs 151
 
  • #9
well, i just got out of fernandos seminar. the talk was about obtaining Yukawa couplings from D6 branes wrapped on toroidal compactifications. also, some talk of orbifold compactifications.

some stuff at the end about the Fukawa category which sounded really interesting, but i didn t follow.

things i need to understand before i can follow fernando s work include:

kähler manifolds
sheaves
supersymmetry/supergravity
instantons and solitons

in other words, a lot of stuff.

if you want to see the slides from his talk, it might give you an idea of the flavor of his thesis, since it is on the same subject. you can see them http://uw.physics.wisc.edu/~strings/group/slides/marchesano2003.ps [Broken]
 
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1. What is the Standard Model from Intersecting Branes?

The Standard Model from Intersecting Branes is a theoretical model in particle physics that attempts to explain the fundamental particles and interactions in the universe. It is based on the idea that our universe is made up of multiple dimensions, and that particles and forces can arise from the interactions of strings in these dimensions.

2. How does the Standard Model from Intersecting Branes differ from the traditional Standard Model?

The Standard Model from Intersecting Branes differs from the traditional Standard Model in that it incorporates the concept of extra dimensions. The traditional Standard Model is based on three dimensions of space and one dimension of time, while the Intersecting Branes model proposes that there are additional dimensions that can influence the behavior of particles and forces.

3. What are the main predictions of the Standard Model from Intersecting Branes?

The Standard Model from Intersecting Branes predicts the existence of additional particles, such as gravitons and Kaluza-Klein particles, which could help explain the nature of dark matter. It also predicts new interactions between particles, which could potentially be observed in experiments.

4. Has the Standard Model from Intersecting Branes been tested experimentally?

While there is currently no direct evidence for the Standard Model from Intersecting Branes, some of its predictions have been tested and confirmed in experiments. For example, the discovery of the Higgs boson at the Large Hadron Collider supports the idea of a Higgs field, which is a key component of the Intersecting Branes model.

5. What are the current challenges and limitations of the Standard Model from Intersecting Branes?

One of the major challenges of the Standard Model from Intersecting Branes is the lack of experimental evidence to support its predictions. Additionally, the model is still incomplete and does not fully explain all observed phenomena, such as the hierarchy problem and the nature of dark matter. Further research and experimentation are needed to fully understand and validate this model.

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