road to the mssm thru m theory ? stuart raby university of michigan ann arbor may 5, 2007
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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 6
Phenomenology
charge quantization gauge coupling unification Yukawa unification neutrino masses
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 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
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 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 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 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 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 !!
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