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The discrete beauty of local GUTsHans Peter Nilles
Physikalisches Institut
Universitat Bonn
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 1/33
Outline
Evidence for grand unification and
the usefulness of global U(1) symmetries
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 2/33
Outline
Evidence for grand unification and
the usefulness of global U(1) symmetries
require a consistent UV-completion of the theory!
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 2/33
Outline
Evidence for grand unification and
the usefulness of global U(1) symmetries
require a consistent UV-completion of the theory!
string theory supplies
the concept of local grand unificationdiscrete symmetries
moduli stabilization and Susy breakdown
fluxes, gaugino condensation and upliftinggravity and mirage mediation
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 2/33
GUT evidence
Experimental findings suggest the existence of two newscales of physics beyond the standard model
MGUT ∼ 1016GeV and MSUSY ∼ 103GeV:
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 3/33
GUT evidence
Experimental findings suggest the existence of two newscales of physics beyond the standard model
MGUT ∼ 1016GeV and MSUSY ∼ 103GeV:
Neutrino-oscillations and “See-Saw Mechanism”
mν ∼ M2W /MGUT
mν ∼ 10−3eV for MW ∼ 100GeV,
Evolution of couplings constants of the standard modeltowards higher energies.
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 3/33
The fate of global symmetries
Global U(1) symmetries are very useful for
absence of FCNC (solve flavour problem)
Yukawa textures à la Frogatt-Nielsen
solutions to the µ problem
axions and the strong CP-problem
R-symmetry and proton stability
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 6/33
The fate of global symmetries
Global U(1) symmetries are very useful for
absence of FCNC (solve flavour problem)
Yukawa textures à la Frogatt-Nielsen
solutions to the µ problem
axions and the strong CP-problem
R-symmetry and proton stability
But they might be destroyed by gravitational effects:
we need a UV-completion of the theory
with a consistent incorporation of gravity
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 6/33
String theory as a UV-completion
What do we get from string theory?
supersymmetry
extra spatial dimensions
(large unified) gauge groups
consistent theory of gravity
many discrete symmetries
but no global continuous symmetries
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 7/33
String theory as a UV-completion
What do we get from string theory?
supersymmetry
extra spatial dimensions
(large unified) gauge groups
consistent theory of gravity
many discrete symmetries
but no global continuous symmetries
String theory could serve as the UV-completion with aconsistent incorporation of gravity,but we need to make contact with the real world (MSSM).
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 7/33
Local Grand Unification
In fact string theory gives us a variant of GUTs
complete multiplets for fermion families
split multiplets for gauge- and Higgs-bosons
partial Yukawa unification
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 8/33
Local Grand Unification
In fact string theory gives us a variant of GUTs
complete multiplets for fermion families
split multiplets for gauge- and Higgs-bosons
partial Yukawa unification
Key properties of the theory depend on the geographyof the fields in extra dimensions.
This geometrical set-up called local grand unification,can be realized in the framework of the
“heterotic braneworld”.(Förste, HPN, Vaudrevange, Wingerter, 2004; Buchmüller, Hamaguchi, Lebedev, Ratz, 2004)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 8/33
Localized gauge symmetries
SU(6)×SU(2)
SU(6)×SU(2)
SO(10)
SU(4)2
(Förste, HPN, Vaudrevange, Wingerter, 2004)The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 9/33
Standard Model Gauge Group
SU(6)×SU(2)
SU(6)×SU(2)SU
(3) 2
SU(5)
SU(4)×SU(2)2
SO(10)
SU(4)2
SU
(4)×
SU
(2)2
SU(5)S
U(3) 2
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 10/33
The Heterotic Braneworld
many models with the exact spectrum of the MSSM(absence of chiral exotics)
(Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007-2009)
local grand unification (by construction)
gauge- and (partial) Yukawa unification(Raby, Wingerter, 2007)
examples of neutrino see-saw mechanism(Buchmüller, Hamguchi, Lebedev, Ramos-Sanchez, Ratz, 2007)
models with R-parity + solution to the µ-problem(Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007)
gaugino condensation and mirage mediation(Löwen, HPN, 2008)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 11/33
Symmetries
String theory gives us
gauge symmetries
discrete global symmetries from geometry and stringyselection rules (Kobayashi, HPN, Plöger, Raby, Ratz, 2006)
accidental global U(1) symmetries in the low energyeffective action
(Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 12/33
Symmetries
String theory gives us
gauge symmetries
discrete global symmetries from geometry and stringyselection rules (Kobayashi, HPN, Plöger, Raby, Ratz, 2006)
accidental global U(1) symmetries in the low energyeffective action
(Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008)
We might live close to a fixed point with enhancedsymmetries that explain small parameters in the low energyeffective theory.
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 12/33
Location matters
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 13/33
Symmetries
String theory gives us
gauge symmetries
discrete global symmetries from geometry and stringyselection rules (Kobayashi, HPN, Plöger, Raby, Ratz, 2006)
accidental global U(1) symmetries in the low energyeffective action
(Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008)
We might live close to a fixed point with enhancedsymmetries that explain small parameters in the low energyeffective theory.
These symmetries can be trusted as we are working withina consistent theory of gravity.
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 14/33
Applications of global symmetries
Applications of discrete and accidental global symmetries:
(nonabelian) family symmetries (and FCNC)(Ko, Kobayashi, Park, Raby, 2007)
Yukawa textures (via Frogatt-Nielsen mechanism)
a solution to the µ-problem(Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2007)
creation of hierarchies(Kappl, HPN, Ramos-Sanchez, Ratz, Schmidt-Hoberg, Vaudrevange, 2008)
proton stability via “Proton Hexality”(Dreiner, Luhn, Thormeier, 2005; Förste, HPN, Ramos-Sanchez, Vaudrevange, 2010)
approximate global U(1) for a QCD accion(Choi, Kim, Kim, 2006; Choi, HPN, Ramos-Sanchez, Vaudrevange, 2008)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 15/33
A Benchmark Model
At the orbifold point the gauge group is
SU(3) × SU(2) × U(1)9 × SU(4) × SU(2)
one U(1) is anomalous
there are singlets and vectorlike exotics
decoupling of exotics and breakdown of gauge grouphas been verified
remaining gauge group
SU(3) × SU(2) × U(1)Y × SU(4)hidden
for discussion of neutrinos and R-parity we keep alsothe U(1)B−L charges
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 16/33
Spectrum
# irrep label # irrep label
3 (3,2;1,1)(1/6,1/3) qi 3`
3,1;1,1´
(−2/3,−1/3)ui
3 (1,1;1,1)(1,1) ei 8 (1,2;1,1)(0,∗) mi
3 + 1`
3,1;1,1´
(1/3,−1/3)di 1 (3,1;1,1)(−1/3,1/3) di
3 + 1 (1,2;1,1)(−1/2,−1) ℓi 1 (1,2;1,1)(1/2,1) ℓi
1 (1,2;1,1)(−1/2,0) hd 1 (1,2;1,1)(1/2,0) hu
6`
3,1;1,1´
(1/3,2/3)δi 6 (3,1;1,1)(−1/3,−2/3) δi
14 (1,1;1,1)(1/2,∗) s+i 14 (1,1;1,1)(−1/2,∗) s−i
16 (1,1;1,1)(0,1) ni 13 (1,1;1,1)(0,−1) ni
5 (1,1;1,2)(0,1) ηi 5 (1,1;1,2)(0,−1) ηi
10 (1,1;1,2)(0,0) hi 2 (1,2;1,2)(0,0) yi
6 (1,1;4,1)(0,∗) fi 6`
1,1;4,1´
(0,∗)fi
2 (1,1;4,1)(−1/2,−1) f−
i 2`
1,1;4,1´
(1/2,1)f+
i
4 (1,1;1,1)(0,±2) χi 32 (1,1;1,1)(0,0) s0i
2`
3,1;1,1´
(−1/6,2/3)vi 2 (3,1;1,1)(1/6,−2/3) vi
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 17/33
Unification
Higgs doublets are inuntwisted (U3) sector
heavy top quark
µ−term protected by adiscrete symmetry
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17log10 H�GeVL
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
Αi
Α3
Α2
Α1
Αt
threshold corrections (“on third torus”) allow unificationat correct scale around 1016 GeV
natural incorporation of gauge-Yukawa unification(Hosteins, Kappl, Ratz, Schmidt-Hoberg, 2009)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 18/33
Hidden Sector Gaugino Condensation
2 4 6 8 10 12 14 16log10 HL�GeVL
0
5
10
15
20
25
#of
mod
els
Gravitino mass m3/2 = Λ3/M2
Planckand Λ ∼ exp(−S)
(Lebedev, HPN, Raby, Ramos-Sanchez, Ratz, Vaudrevange, Wingerter, 2006)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 19/33
Dilaton (Modulus) Domination
This leads to a variant the “gravity mediation” scenario,
but we still have to adjust the vacuum energy.
Here we need a “downlifting” mechanism:
“downlifting” mechanism can fix S as well (no need fornonperturbative corrections to the Kähler potential)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 20/33
Downlift
(Löwen, HPN, 2008)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 21/33
Dilaton (Modulus) Domination
This leads to a variant the “gravity mediation” scenario,
but we still have to adjust the vacuum energy.
Here we need a “downlifting” mechanism:
“downlifting” mechanism can fix S as well (no need fornonperturbative corrections to the Kähler potential)
(Löwen, HPN, 2008)
gives a suppression factor log(m3/2/MPlanck)(Choi, Falkowski, HPN, Olechowski, 2005)
mirage mediation: mixed modulus-anomaly mediationfor the gaugino masses
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 22/33
Evolution of couplings
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17log10 H�GeVL
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09Α
i
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 23/33
Mirage Scale
102 104 106 108 1010 1012 1014 1016
0.4
0.6
0.8
1
1.2
Μ @GeVD
Mas
s@T
eVDΑ = 1 m3�2 = 20 TeV Φ = 0
M1
M2
M3
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 24/33
Can we test this at the LHC?
At the LHC we scatter
protons on protons, i.e.
quarks on quarks and/or
gluons on gluons
Thus LHC will be a machine to produce strongly interactingparticles. If TeV-scale SUSY is the physics beyond thestandard model we might expect LHC to become a
GLUINO FACTORY
with cascade decays down to the LSP neutralino.
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 25/33
The Gaugino Code
Mixed boundary conditions at the GUT scalecharacterized by the parameter α:the ratio of modulus to anomaly mediation.
M1 : M2 : M3 ≃ 1 : 2 : 6 for α ≃ 0
M1 : M2 : M3 ≃ 1 : 1.3 : 2.5 for α ≃ 1
M1 : M2 : M3 ≃ 1 : 1 : 1 for α ≃ 2
M1 : M2 : M3 ≃ 3.3 : 1 : 9 for α ≃ ∞
The mirage scheme leads to
LSP χ01
predominantly Bino
a “compact” gaugino mass pattern.(Choi, HPN, 2007; Löwen, HPN, 2009)
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 26/33
Gaugino Masses
0 1 2 3 5 10 ¥
-3
-2
-1
0
1
2
3
Α
Ma�ÈM
0ÈH
1+Α
2L1�2
M1
M2
M3
Mod
ulus
Anom
aly
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 27/33
Scalar Masses
0 1 2 3 5 10 ¥
-0.5
0
0.5
1
1.5
Α
mi2�ÈM
02H1+Α
2L
qL
eR
{LM
odul
us
Anom
aly
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 28/33
Scalar Masses
0 1 2 3 5 10 ¥
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Α
mi2�ÈM
02H1+Α
2L
qL
eR
{L
Mod
ulusw
Anom
alyw
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 29/33
Constraints onα
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
0
10
20
30
40
50
60
Α
m3�
2@T
eVD
tan Β = 30 Ξ = 1�3 Φ = 0
TACHYONS
t�LS
PBelow LEP
W > WWMAP
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 30/33
Constraints onα (modified mirage)
an Β � 30 Ηi �t 3
0 1 2 3 4 5 6 7 8
0
10
20
30
40
50
60
�3�
2�T
eVm
Α
g�
LSP
No EWSB
Χ� + LSP
BelowLEP BelowLEP
t�LS
P�+
LSP
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 31/33
Conclusion
String theory might provide us with a consistentUV-completion of the MSSM including
Local Grand Unification
Accidental symmetries (of discrete origin)
Geography of extra dimensions plays a crucial role:
gauge-Yukawa unification and a naturally heavy top
gravity-mirage mediation without a “flavour problem”
We seem to live at a special place in the extra dimensions!
The LHC might clarify the case for (local) grand unification.
The discrete beauty of local grand unification, PLANCK10, CERN, June 2010 – p. 32/33
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