Road to the MSSM thru M theory ?

Stuart Raby

University of MichiganAnn Arbor

May 5, 2007

Phenomenology

charge quantization gauge coupling unification Yukawa unification neutrino masses

Title of talk 3

uu u u

e

u uQ

ddQ

d dd ed

q u du

u d

l

uu d

ee

udd

u

dd

3

2EM LYQ T

Pati-Salam SU(4)CxSU(2)LxSU(2)R

32 RY B L T

(5) (1)

(10)

(4)

(2) (2)L R

SU U

SO

SU SU SU

31 510 5 1

16

Q + Q

1 1 1 1 12 2 2 2 2

16 even( , , , , ) no. minus signsodd16

45 ( 1, 1,0,0,0)

10 ( 1,0,0,0,0) Cartan-Weyl

Title of talk 5

spinor repsn.of SO( 10 )

Charge quantization

Title of talk 6

Phenomenology

charge quantization gauge coupling unification Yukawa unification neutrino masses

Title of talk 7

Gauge coupling unification

163 10 GeVGM

Title of talk 8

Phenomenology

charge quantization gauge coupling unification Yukawa unification neutrino masses

Title of talk 9

Phenomenology

charge quantization gauge coupling unification Yukawa unification neutrino masses

Title of talk 10

Phenomenology

charge quantization gauge coupling unification Yukawa unification neutrino masses

SO(10) SUSY GUT w/ L.E. SUSY

Title of talk 11

4 D GUT problems

GUT symmetry breaking

Higgs doublet – triplet splitting

Solution ?

Orbifold GUTs

Orbifold SUSY GUTs in 5 or 6D

N=2 N=1 SUSY chiral gauge theory gauge symmetry breaking Higgs doublet-triplet splitting

All this first observed in heterotic string in 10D

Title of talk 13

Outline

Orbifold GUTs / String Orbifolds Kobayashi, SR, Zhang hep-ph/0403065 , hep-ph/0409098 Mini-Landscape search for MSSM LNR3VW hep-th/0611095, hep-th/0611203 The road from M theory

Title of talk 14

E8 x E8 heterotic string

Constructing MSSM / 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 15

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 16

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

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

E6 GUT in 5 or 6D

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 Z i Z

Massless Untwisted sector P2 = 21

6 3 66

3 3

13 3

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

, (0,1,0,0)

(0,1, 1,0) twist

V V V

P V r v Z r

v

GSO

Gauge lattice

Title of talk 18

1 1 1 1 1 1 1 12 2 2 2 2 2 2 2

(0,0,0, 1, 1,0,0,0) 45

16 ( , , , , , , , ) 16

( 1, 1,0,0,0,0,0,0) 8

P

3 Consider P V Z

E(6) x SU(3) , 78,1 1,8V

1 2Similarly 27, 27 U , U

Gauge & U3

Title of talk 19

Then add Z2 orbifold + W2 [in long direction]

E6 SO(10) SU(4)xSU(2)LxSU(2)R

F3 = (4,2,1), F3c = (4c,1,2) , H = (1,2,2)

P P’ ( V2 ) ( V2+ W2 )

Title of talk 20

T1 twisted sector

2 Light fam’s

Vector-like exotics

Local SO(10)

Title of talk 21

3rd family in bulk gauge-Yukawa unification

1st and 2nd families on Z2 fixed points

D4 family symmetry

Higgs for PS symmetry breaking

53 3

0

27 27R

cgdy gHF F

R

To summarize

S1/Z2

161162

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 3f singlet

geometry space group sel. rule

Title of talk 24

Fermion mass hierarchy

Title of talk 25

Mini-Landscape searchhep-th/0611095

Lebedev, Nilles, SR, Ramos-Sanchez,

Ratz, Vaudrevange & Wingerter

Title of talk 26

Buchmuller, Hamaguchi, Lebedev & Ratz Z6-II orbifold

Looked for and found SM gauge group in 4D with

3 families and vector-like

exotics

Search for MSSM Spectra in heterotic orbifolds

Title of talk 27

Mini-Landscape search Z6-II orbifold1. V6 breaks to SO(10) [or E(6)]

2. 2 families [ 16 [or 27] ] in T1 twisted sect. 3. Generate 2 Wilson lines W3 , W2 4. Identify ‘inequivalent’ models5. Select models with6. Select models with 3 net (3,2)7. Select models with non-anom.8. Select models with 3 SM families + Higgses + vector-like exotics

(5) (10)SMG SU SO

1( ) (5)U Y SU

Title of talk 28

Mini-Landscape search LNRRRVW

Title of talk 29

Mini-Landscape search LNRRRVW

93 MSSM-like models orprobability ~ 1/300

‘Fertile’ patch in heterotic landscape !!

Title of talk 30

Low Energy Supersymmetry from the Heterotic Landscape

hep-th/0611203

Lebedev, Nilles, SR, Ramos-Sanchez,

Ratz, Vaudrevange & Wingerter

Title of talk 31

Low Energy SUSY Breaking LNRRRVW

Step 8 : 77 models

Title of talk 32

Number of models vs. the size of largest gauge group in the hidden sector. N labels SU(N), SO(2N), E(N) groups.

The background corresponds to Step 2, while the foreground corresponds to Step 8.

The background corresponds to Step 2, while the foreground corresponds to Step 6.

Title of talk 33

Gluino condensate

22

3 3

1 1 1 exp , Re 2

3 exp 2

GUTGUT

GUT

Mgg M

M

S

SW

Assume stabilize S in Kahler potential

Re 2S & take

Title of talk 34

Number of models vs. scale of gaugino condensation.

3 3/ 2 13

3

2 10 GeV10 GeV

Pl

mM

Title of talk 35

LNRRRVW - in progress

1. Check for D = F = 0 directions2. Check all exotics get mass3. Check fermion masses4. Check Rparity conservation5. Check neutrino masses ( 4 & 5

related ) 3( B – L) = 0 mod 2 “Family

reflection

symmetry” SUSY breaking and lifting flat

directions ??

Title of talk 36

The road from M theory

11 dim. Supergravity on R3,1 x X7

X7 has G2 holonomy

Non-Abelian gauge fields on singularities with co-dimension 4 eg. X7 = K3 x T3 with singular points in K3

Title of talk 37

E8 x E8 heterotic limit

Horava - Witten11 dim. Supergravity on R3,1 x X6 x S1/Z2

X6 has SU3 holonomy

Non-Abelian gauge fields on two10 dim end-of-the-world branes

Title of talk 38

E8 x E8 heterotic limit

Compactify X6 eg. X6 = (T2)

2 / Z3 x T2

& add Wilson line W3 K3 fixed points ? E(6) in 6 dim.

Title of talk 39

CY3 w/ K3 fibration in type II dual to

K3 x T2 = T4 / ZN x T2 in heterotic Kachru & Vafa hep-th/9505105Vafa & Witten hep-th/9507050 Aldazabal, Font, Ibanez & Quevedo hep-th/9510093 Candelas & Font hep-th/9603170Bershadsky, Intriligator, Kachru, Morrison, Sadov & Vafa hep-th/9605200 use F theory

Title of talk 40

Barshefsky, Intriligator, Kachru, Morrison, Sadov & Vafa

Title of talk 41

F theory on heterotic/type II duality

Compactified on K3 x T2Bershadsky, Intriligator, Kachru, Morrison,Sadov & Vafa hep-th/9605200

E8 w/ 10 instantons E6

+ 4 (27 + c.c.)E8 w/ 14 instantons SO10

+ 6 (16 + c.c.) + 8 (10 + c.c.)

K3 + instantons = T4 / Z3 + Wilson line !!!

Title of talk 42

On the Duality between perturbative heterotic orbifolds and M theory on T4/ZN [ orbifold limit of K3 ]

X6 = T4 / ZN x T2 w/N = 2, 3, 4, 6

dual to X7 = T4 / ZN x T2 x S1 / Z2

Kaplunovsky, Sonnenschein, Theisen &Yankielowicz hep-th/9912144Faux, Lust & Ovrut hep-th/0010087

Title of talk 43

On the Duality between heterotic on T3 x R6,1 and M theory on K3 x R6,1

Is there a useful duality between E(8)xE(8) heterotic on T4 x T2 x R3,1 orbifolded and M theory on K3 x S1 x [ S2 x

R3,1 ] ??

Acharya & Gukov hep-th/0409191

Title of talk 44

String threshold corrections & Gauge coupling unification

Ibanez & Lust hep-th/9202046

Calculate moduli dependence of string threshold corrections Show : Only certain orbifolds with T1 >> T2 , T3 are consistent with MGUT < Mstring

Z6-II, Z8 & ZN x ZM !!

Title of talk 45

Conclusions

We find MSSM in ‘fertile patch’ of E(8)xE(8) heterotic string compactified on orbifold [(T4 / Z3) x T2 ]/Z2

IS there an M theory dual ?? use to understand moduli stabilization and SUSY breaking a la Acharya et al.

Important to test string theory