title of talk1 a fertile patch in the heterotic landscape stuart raby rutgers university march 24,...
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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 ??
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