Title of talk 1

A Fertile Patch in the Heterotic Landscape

Stuart Raby

Rutgers UniversityMarch 24, 2009

Title of talk 2

Kobayashi, Raby, Zhang hep-ph/0403065 , hep-ph/040909Buchmuller, Hamaguchi, Lebedev & Ratz hep-ph/0511035, hep-ph/0512326Lebedev, Nilles, Raby, Ramos-Sanchez, Ratz, Vaudrevange & Wingerter hep-th/0611095, hep-th/0611203, 0708.2691[hep-th]Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/0611020Dundee, Raby & Wingerter arXiv:0805.4186 [hep-th]Dundee & Raby arXiv:0808.0992 [hep-th]

Title of talk 3

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 4

String Model Building Orbifold GUTs Local GUTs 3 = 2 + 1 “Benchmark” model Local SO(10) & SU(6) orbifold GUT Gauge-Higgs unification Ytop = gGUT

Exact R-parity Vector-like exotics & extra U(1)s decouple in SUSY limit D4 family symmetry Gauge coupling unification & more …

Title of talk 5

Constructing MSSM from heterotic string/ Caveats

SUSY solution at MS

100’s moduli ( geometric & more )

moduli stabilization & SUSY breaking ?? save for later

gauge & Yukawa couplings fcns. of moduli tune to desired values

Title of talk 6

Standard Model =

Where would you look ??

In this landscape ?

Or in a golf course ! = GUT

Title of talk 7

Perform focused search “Mini Landscape” Lebedev, Nilles, Raby, Ratz, Ramos-Sanchez,

Vaudrevange & Wingerter Use both Local & Orbifold GUTs Find ~ 200 MSSM-like models Consider properties of one “Benchmark” model

See what MSSM-like means !

Outline

Title of talk 8

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 9

Untwisted

T1,5 twisted

T2,4 twisted

T3 twisted

16 66 (1,2, 3,0), Z exp 2 Zi i iv iv

Title of talk 10

Mini-Landscape search Z6-II orbifold V6 breaks to SO(10) [or E(6)]

2 families [ 16 [or 27] ] in T1 twisted sect. 1. Generate 2 Wilson lines W3 , W2 2. Identify ‘inequivalent’ models3. Select models with4. Select models with 3 net (3,2)5. Select models with non-anom.6. Select models with 3 SM families + Higgses + vector-like exotics

(5) (10)SMG SU SO

1( ) (5)U Y SU

Title of talk 11

Mini-Landscape search LNRRRVW

218 Models with 3 families, Higgs &

vector-like exotics

Title of talk 12

Road to the MSSM with R-parityLNRRRVW – 0708.2691[hep-th]

1. Check for D = 0 directions 2. Check R parity 3. Check all exotics get large mass4. Check light Higgs 5. Check charged fermion masses 6. Check neutrino masses 7. Check dimension 5 B & L

violating ops.

Title of talk 13

D = 0

D = 0 is not a significant constraint

Title of talk 14

Generalized R parity

i B LR e

2Z Forbid Dim 2 & 3 operators

Family Reflection symmetry or Matter parity

3

23f

- 2 /B L f f

Title of talk 15

Construct model w/ Generalized R parity

0, 2, 2/3, 2/5, 4/5, 2/7, 4/7, ....f

Identify “suitable” B-L standard for SM particles vector-like on exotics maximal no. SM singlets w/

Title of talk 16

Results

Title of talk 17

1 1 11 2 8 1 2 82 2 2

8

ii=1

(8)

( , ,..., ), ( , ,..., )

1,...,8 n 2i

P E

P n n n n n n

n i

Z Z

1 1 16 3 2 2( , , ,0,0,0,0,0)V

Gauge lattice

1 1 1 1 1 1 1 13 2 2 6 6 6 6 6 6( , , , , , , , )W

1 1 1 12 2 2 2 2(0, , , , ,0,0,0)W

Embed twist in gauge lattice via shift

Wilson lines

Benchmark Model

Title of talk 18

Local SO(10) GUT

22 1L 62m ' 1 0P V a

26=2,

0,0,0, 1, 1,0,0,0 0, 1, 1,0,0,0,0,0

Local SO(10) SO(4) GUT

P P V

P

Z

Require massless SO(10) spinors at T1 fixed points

Mass operator

Title of talk 19

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 20

Consider massless Untwisted sector P2 = 2

1 1 1

6 3 63 2 2

3 3

13 3

( , , ,0,0,0,0,0), 2

, 0,1,0,0

(1, 1,0,0) twist

V V V

P V r v r

v

Z

GSO projection

Orbifold GUTs

Gauge U3

Title of talk 21

(0, 1, 1,0,0,0,0,0) SO(14) P UUUUUUUUUUUUUU

3 Consider P V Z

(V, ) 35

1 2Similarly 20 20 U , Uc

Gauge & U32

3 6 32 ( , 1, 1,0,0,0,0,0)V V

3P W Z (0,0, 1, 1,0,0,0,0) SU(6) P UUUUUUUUUUUUUU

1 1 1 1 1 1 1 13 2 2 6 6 6 6 6 6( , , , , , , , )W

Gauge & U3

Title of talk 22

Then add Z2 orbifold + W2 [in long direction]

SU(6)

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

P P’

( V2 ) ( V2+ W2 )2 lightfamilies

Title of talk 23

2 (16) on SO(10) brane

Title of talk 24

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 25

Discrete non-Abelian Family

symmetry

Title of talk 26

S1/Z2

161162

Title of talk 27

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 28

Fermion mass hierarchy

Title of talk 29

Discrete Family Symmetries

Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/0611020

See also: D4 phenomenologyKo, Kobayashi, Park & Raby arXiv:0704.2807

Title of talk 30

Benchmark model

S

Title of talk 31

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 32

term

0 1 1SW = 0 in flat space SUSY limit

Yukawa couplings

Neutrino masses via See-Saw

Not realistic - yet

Title of talk 33

Gauge coupling unification

1MC

Title of talk 34

1 1 2GUT log

2

MSSMstring heavy loop lighti

i Z string i i iZ

MbM M

M

2 ,loop lighti i 2 loop and weak scale corr’s

log 1

4 2

Gi i string stringheavy

iC C

b b M Mb

M M

KKmodes

log2

EXstringi

EX

Mb

M exotics

RG equations

Title of talk 35

In this SU(6) orbifold GUT with gauge-Higgs unificationthe KK modes do NOT focus gauge couplings to unify at Mstring

Therefore NEED exotics with massMEX < MC

Title of talk 36

Gauge coupling unification

2

21

GUT18

Pl

string

MM

1GUT 62

Title of talk 37

Proton Decay

observable ?

Title of talk 38

2

string GUT7

8eg =

2

string

C

M

M

10D string coupling Dundee & Raby

following Hebecker & Trapletti

WeakCoupling !!

Title of talk 39

After first Z3 orbifold + Wilson line W3

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

2 / Z3 x T2

Obtaining the same theory by compactifying E8 x E8 heterotic

string on ‘smooth’ CY3 manifold ?

V, 35 SU(6) adjoint

20 20 18 6 6c c

Title of talk 40

6H V TN N 29 N 273

320 76 29(1) 273

Satisfies Gravity anomalyconstraint

Complete spectrum of 6D SU(6) orbifold GUT

Title of talk 41

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 !!

F-theory CY3 [T2 fibration over Fn] xT2

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

Title of talk 42

Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa

r 2

n = 0

Title of talk 43

Derivable from a dual F theory construction ??

Work in progressWe 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 44

Conclusions

We find MSSM in “fertile” patch of E(8)xE(8) heterotic string

Important to test string theory

SUSY breaking and lifting flat directions ??

Almost realistic “Benchmark” models !!! w/ Caveat

Orbifold & Local GUT MSSMDerivable from F theory dual ??