Standard Model from Intersecting Branes?

[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

 

[Mentat]

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?

 

[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.

 

[marcus]

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

 

[lethe]

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.

 

[lethe]

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.

 

[selfAdjoint]

Super! Maybe you can bring us some news?

 

[selfAdjoint]

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 Eective 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

 

[lethe]

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