Title of talk 1

String Model Building

Stuart Raby

String Pheno 09Warsaw University

June 19, 2009

Savoy Hotel München I Amalienstraße 25 I 80333 München

Title of talk 2

Outline Random searches for the MSSM Virtues of SUSY GUTs Heterotic model building Smooth manifolds & Free fermions Orbifolds F theory / Type IIB Heterotic - F theory duals Conclusion

String Model Buildingor Searching for the MSSM

Title of talk 3

Random Searches for the MSSM

9

1 :10

41 :10

Type II intersecting D brane models

Gepner orientifolds

Heterotic free fermion landscape analysis

Gmeiner, Blumenhagen, Honecker, Lust & Weigand

Anastasopoulos, Dijkstra, Kiritsis & Schellekens

Dienes, Lennek, Senechal & Wasnik

MSSM is quite rare !!

Title of talk 4

Virtues of SUSY GUTs MZ << MGUT “Natural” Explains charge quantization Predicts gauge coupling unification !! Predicts SUSY particles at LHC ! Predicts proton decay Predicts Yukawa coupling unification w/Family symmetry Fermion mass hierarchy Neutrino masses and mixing via See-Saw LSP - Dark Matter candidate Baryogenesis via leptogenesis

Title of talk 5

Standard Model =

Where would you look ??

In this landscape ?

Or in a golf course ! = GUT

Title of talk 6

E8 x E8 Heterotic models

Smooth CY3

Free fermions

Orbifold

Title of talk 7

E8 x E8 Heterotic models

Smooth CY3

Bouchard & Donagi ( & Cvetic)

SU(5) GUT

Wilson line breaking to SM gauge group

Higgs doublet – triplet splitting

Title of talk 8

E8 x E8 Heterotic models

Smooth CY3

SM gauge group 3 families 1 or 2 pairs ( Hu + Hd )

0

0u ed

a b c

b d e

c e

R parity cons.

Function of moduliNeed non-pert. physics

Title of talk 9

E8 x E8 Heterotic models

Free fermionic

SM gauge group 3 families 1 pair ( Hu + Hd )

Cleaver, Faraggi, Nanopoulos (& Walker) 1998

Vector-like exotics decoupleNon trivial Yukawa matrices &Neutrino See-Saw

Title of talk 10

E8 x E8 Heterotic models

Orbifolds

Dixon, Harvey, Vafa & Witten Font, Ibanez, kim, Nilles, Quevedo

Kobayashi, Raby & Zhang Buchmuller, Hamaguchi, Lebedev & Ratz Lebedev, Nilles, Raby, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter Kim, Kim & Kyae

Title of talk 11

Mini-Landscape search LNRRRVW

223 Models with 3 families, Higgs

& ONLY vector-like exotics

Out of ~ 30,000 models

1 :100

Fertile patch in Heterotic landscape

Title of talk 12

E8 x E8 heterotic string in 10DCompactify 6D on

(T2)3

Then mod by Z6-II = (Z3 x Z2) and Add Wilson lines

Z6 embedded in E8 x E8 gauge latticeas shift V6 : consistent with mod. inv. !

Title of talk 13

First consider (T2)3/Z3 + W3 [Wilson line in SU3 torus]

Massless modesFrom Untwisted sector + (G2 , SU3) twisted sector

SU(6) GUT in 5 or 6D

V, 35 SU(6) adjoint

20 20 18 6 6c c

Orbifold GUTs

Title of talk 14

Then add Z2 orbifold + W2 [in long direction]

SU(6)

SU(5) SU(3)xSU(2)xU(1)

P P’

( V2 ) ( V2+ W2 )

Title of talk 15

Local SO(10) GUT2 lightfamilies

Two 4D fixed points are special !!

Title of talk 16

2 (16) on SO(10) brane

Title of talk 17

Third family & Higgs in BULK

3 3 3 2 3 1 3 3 3 2 3 1

2 3 2 2 2 1 2 3 2 2 2 1

1 3 1 2 1 1 1 3 1 2 1 1

H

H

u

d

V V V

V V V

V V V

3

3

Q t(20

L

20 )

2 6 b

6

c

c

GUT 35

0

gdy 20 0 g Q H t2

Rc

uWR

Title of talk 18

Discrete non-Abelian Family

symmetry

Title of talk 19

S1/Z2

161162

Title of talk 20

D4 family symmetry 4 1 3 2

1 1 2 3 2 2

1, , ,

0 1 1 0: :

1 0 0 1

D i

f f f f

1

2

f

f

doublet 3 , H ,Hu df singlets

geometry space group sel. rule

Title of talk 21

Fermion mass hierarchy

Natural Froggatt-Nielsen mechanism !

Title of talk 22

Benchmark model

S

Title of talk 23

Exact R-parity !!

U(1)B-L broken to Z2 matter parity

UDD, LLE, QLD, LHu

F -F, H H

Forbids R-parity violating operators

0

Title of talk 24

term

0 1 1SW = 0 in flat space SUSY limit

Yukawa couplings

Neutrino masses via See-Saw

Not realistic - yet

Title of talk 25

Note: Yukawa couplings, gauge couplingsand Vector-like exotic masses are functions of moduli (along SUSY flatdirections).

Some of these moduli are blow up modesfor some, BUT NOT ALL, of the orbifoldfixed points.

2 fixed points are not blown up !!

Title of talk 26

F theory / Type IIB models Beasley, Heckman & Vafa Donagi & Wijnholt Blumenhagen, Braun, Grimm & Weigand Chen & Chung Marsano, Saulina & Schaefer-Nameki

• SU(5) GUT on D7 brane / • Chiral matter in 6D /• Yukawa couplings at triple intersect’n of matter branes –• Fermion flavor hierarchy natural

3,1S R3,1R

1 2 3

Title of talk 27

Gauge 7-brane /

Matter 7-brane /

3,1S R

3,1'S R

'S S

Title of talk 28

F theory / Type IIB models

• SU(5) breaks to SM gauge group with <FY> : hypercharge flux Not possible in Heterotic string !

• <FY> on Higgs brane doublet-triplet splitting• Spinor reps of SO(10) possible ! Not possible in perturbative IIB

10 2( ) higgsing hyperchargeY Yd x dB A F

Title of talk 29

F theory / Type IIB models

Heckman & Vafa Randall & Simmons-Duffin

8 6 4

6 4 2

4 2

~

1

Due to fluxin 2-3 surfacebreaking geometric flavor symmetry

Title of talk 30

Gravity decouples w/ non-compact z1 direction

Local construction !

Blumenhagen, Braun, Grimm & WeigandMarsano, Saulina & Schaefer-Nameki

global constructions

Title of talk 31

E8 x E8 heterotic - F theory duality

Title of talk 32

Work in progress

We are now attempting to construct the F theory dual to our MSSM-like models. w/ Bobkov, Weigand &

Westphal Find more general description i.e. all models in the same universality class Provide a general understanding of moduli space Help understand moduli stabilization & SUSY breaking ?

Title of talk 33

After first Z3 orbifold + Wilson line W3

we find 6D SU(6) orbifold GUT compactified on (T2)

2 / Z3 x T2

Step 1: E8 x E8 heterotic orbifold on ‘smooth’ CY3 manifold ?

V, 35 SU(6) adjoint

20 20 18 6 6c c

Title of talk 34

6H V TN N 29 N 273

320 76 29(1) 273

Satisfies Gravity anomalyconstraint

Complete spectrum of 6D orbifold GUT

Dundee, Raby & Wingerter

Title of talk 35

Bershadsky, Intriligator, Kachru, Morrison,Sadov & Vafa hep-th/9605200

E8 [12 instantons in SU(3)xSU(2)] SU(6) + (20 + cc) + 18 (6 + c.c.)E8 [12 instantons in E(6) +

higgsing]SO(8) + 4 (8v+ 8s+ 8c + c.c.)

K3 + instantons dual to

T4 / Z3 orbifold + Wilson line !!

E8 x E8 heterotic on K3 x T2 w/instantons

Title of talk 36

Bershadsky, Intriligator, Kachru, Morrison,Sadov & Vafa hep-th/9605200

F-theory CY3 [T2 fibration over Fn] xT2

dual to E8 x E8 heterotic K3 x T2 w/instantons

visible SU(6)

20 + 18 (6)

Title of talk 37

Bulk gauge fields live in 8D& matter fields live in 6D

U1 flux breaksSU(6) toSU(5)

addedfiber &Z2 orb…breaksN=2 toN=1

Title of talk 38

Possible obstruction to findingF theory dual of Heterotic orbifold

modelNeed to keep two orbifold fixed

points -1. Otherwise hypercharge gets

mass Groot Nibbelink, Ha

& Trapletti

2. Wilson line shrinks to point 3. blow up modes on heterotic

side leave 2 orbifold fixed

points

Title of talk 39

Need orbifold fixed points !!Two light families on D3 branes at fixed points ??

Wilsonline in z3

breaksGUT to SM

Orbifold takes torus tosphere

Title of talk 40

Other model building considerations

• Gauge coupling unification• Proton decay from dimension 5 & 6 ops.• Supersymmetry breaking & sparticle masses Heckman & Vafa; Aparicio, Cerdeno & Ibanez• Moduli stabilization • Cosmological constant 10500 vacua ??• Cosmology

Title of talk 41

Conclusions

Several new ideas in string model building

Important to test string theory

Global F theory constructions may openwindow to general MSSM landscape

Orbifold & Local GUT MSSM

Final test at the LHC !