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Title of talk 1
A Fertile Patch in the Heterotic Landscape
Stuart Raby
String PhenomenologyCERN
August 11, 2008
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]
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” LNR3VW (see Wingerter talk) Use both Local & Orbifold GUTs Find ~ 200 MSSM-like models
Consider properties of one “Benchmark” model in this talk
See what MSSM-like means !
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 10
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
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
Title of talk 11
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
Require massless SO(10) spinors at T1 fixed points
Mass operator
Title of talk 12
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
Title of talk 13
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
GSO projection
Orbifold GUTs
gaugeU3
Title of talk 14
(0, 1, 1,0,0,0,0,0) SO(14) P
3 Consider P V
(V, ) 35
1 2Similarly 20 20 U , Uc
Gauge & U32
3 6 32 ( , 1, 1,0,0,0,0,0)V V
3P W (0,0, 1, 1,0,0,0,0) SU(6) P
1 1 1 1 1 1 1 13 2 2 6 6 6 6 6 6( , , , , , , , )W
Gauge & U3
Title of talk 15
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 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 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 22
Discrete Family Symmetries
Kobayashi, Nilles, Ploeger, Raby & Ratz hep-ph/0611020
See also: D4 phenomenologyKo, Kobayashi, Park & Raby arXiv:0704.2807
Title of talk 24
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 25
term 0 1 1W S = 0 in flat space SUSY limit
Yukawa couplings
Neutrino masses via See-Saw
Not realistic - yet
Title of talk 27
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 28
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 31
2
string GUT7
8eg =
2
string
C
M
M
10D string coupling Dundee & Raby
following Hebecker & Trapletti
WeakCoupling !!
Title of talk 32
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 33
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 34
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