Balkan Workshop BW2013 Beyond the Standard Models 25 – 29 April, 2013, Vrnjačka Banja, Serbia

1. Local String Models in
Compact Calabi-Yau
Manifolds and Moduli
Stabilisation
F. Quevedo, ICTP/Cambridge.
SEENET BW2013
April 2013
M.Cicoli, S. Krippendorf, C. Mayrhofer, FQ, R. Valandro:
arXiv:1206.5237 + 1304.2771+ 1304.0022

2. Outline
• Introduction
• Overview of Local Models and LARGE
volume scenario
• Local Models in Compact Calabi-Yau
(D3 and D3/D7 Models)
• The Web of Local Models

3. Introduction

4. Life After the Higgs?
Hierarchy Problem Proposals
• TeV SUSY
• Warped extra dimensions
• Large extra dimensions
• Landscape...
UV complete?
How to break SUSY?
How to fix size of extra dimensions?...

5. SUSY and String Theory
• Strings provide UV completion
• SUSY needed for consistency
• Scale of SUSY breaking?
Sparticle masses: 10-3 eV,…TeV,...,< Mplanck !
Disclaimer: Not necessarily at LHC scale!

6. Generic String Predictions
• Gravity + dilaton+antisymetric tensors+
gauge fields + matter
• SUSY (32,16, … supercharges)
• Extra dimensions (6 or 7)
(flat, small, large, warped?)
• Others? (branes, no csr, dualities,…)

7. Generic 4D String ‘Predictions’
• Moduli (s=0 ‘massless’ fields)
• Antisymmetric tensors:
Branes (brane-world)
Axions (not necessarily QCD axion)
Quantised fluxes!
• If 4D N=1 SUSY: Cosmological Moduli
Problem!? (Mmoduli>10 TeV)
• Only low-dimensional group representations.

9. Challenges for String Models
• Gauge and matter structure of SM
• Hierarchy of scales + masses (including neutrinos)
• Flavor CKM, PMNS mixing, CP no FCNC
• Hierarchy of gauge couplings (unification?)
• ‘Stable’ proton + baryogenesis
• Inflation or alternative for CMB fluctuations
• Dark matter (+ avoid overclosing)
• Dark radiation (Neff>3)
• Dark energy
N.B. If ONE of them does not work, rule out the model!!!

10. Progress in past 10 years
• Model building
Local (branes at singularities, F-theory)
Global (heterotic,…)
• Calculability !!!
e.g.: Non-perturbtive effects (gauge and stringy)
• Moduli Stabilisation (landscape, inflation,…)

11. Model Building

12. String Model Building:
§ Global Models (e.g. Heterotic)
§ Local Brane Models (e.g. IIB)

13. Bottom-up Approach
• Gauge group
• Chiral spectrum
• Yukawa couplings
• Gauge couplings
• Proton stability
• Flavour symmetries
• Moduli Stabilisation
• Cosmological constant
• SUSY Breaking
• Scales (unification,
axions,…)
• Inflation, Reheating
• Cosmological moduli
problem
Local (brane) Properties Global (bulk) Properties
Aldazabal,Ibanez, FQ, Uranga 2000

14. MODULI STABILISATION
4-cycle size: τ
(Kahler moduli)
3-cycle size: U
(Complex structure
moduli)
+ String Dilaton: S
4-cycle size: τ
(Kahler moduli)
3-cycle size: U
(Complex structure
moduli)

15. Exponentially Large Volumes
Exponentially large volume + Broken SUSY!!!
Kahler moduli:

16. Relevant Scales
• String scale Ms=MP/V 1/2
• Kaluza-Klein scale MKK=MP/V 2/3
• Gravitino mass m3/2=W0 MP/V
• Volume modulus mass MV=Mp/V 3/2
• Lighter (fibre) moduli Ml=Mp/V 5/3

17. Original Scenarios
• MString = MGUT~ 1016 GeV (V~105)
• W0~10-11<<1 to get TeV soft terms, or W0~1 and 1010 GeV soft terms ?
• Fits with coupling unification
• Natural scale of most string inflation models.
• Axi-volume quintessence scale (w=-0.999….)
• MString = Mint.~ 1012 GeV (V~1015)
• W0~1
• m3/2~1 TeV (solves hierarchy problem!!!)
• QCD axion scale
• neutrino masses LLHH
• MString = 1 TeV (V~1030)
• W0~1
• Most exciting, 5th Force OK m~10-3 eV, if SM non SUSY. Back reaction?

18. Visible or
Hidden
Sectors
D3 Brane
or
D7 Brane
Where is
the
Standard
Model?

19. LARGE Volume Implies
Standard Model is localised !
( SM D7 cannot wrap the exponentially large cycle
since g2=1/V2/3 ) ‘Bottom-up’ (A
IQU 2000)
§ D3/D7 Branes at a singularity (collapsed cycle)
§ Magnetised D7 - Brane wrapping a ‘small’ four-cycle
§ Local F-Theory

20. D3 Branes at Singularities
• Orbifolds
• Del Pezzos 0-8
(dPn=P2 blown-up at n arbitrary points
c1>0, b2=n+1, 2n-8 parameters, n>3)
• Larger class: Toric singularities
(infinite class of models!!!)

21. Spectrum and couplings
Dimer and Quiver Diagrams (e.g. dP0)
1
2 3

22. Del Pezzo Singularities/Quivers
e.g. del Pezzo 0 (C3/Z3)
ni D3 Branes (group ПU(ni))
mj D7 Branes (group ПU(mi))
Arrows=bi-fundamentals
Anomaly/tadpole cancelation
Hypercharge (ni≠nj)
3 Families!
D7s:Franco-Uranga

23. Standard Models LR-Symmetric Models
Pati-Salam Models Trinification Models

24. Problem for dP0: Yukawa couplings
E-values (M,M,0).
From global flavour symmetry SU(3) (?)
Del Pezzo1 Singularity
SU(2)xU(1) Flavour symmetry
Conlon, Maharana, FQ
Hierarchy in 3 generation masses!!!!
Higgsing gives back dP0!!!

25. e.g. Realistic dP1 Models
Standard Model LR Symmetric Model

26. Generic Features
• Approximate Flavour Symmetries
• Maximum number of families = 3 (toric)
• Quark Mass hierarchy: (M,m,0), M>>m
• Hyperweak Interactions
(SM fields charged under D7 gauge
interactions g2=1/V2/3 <<<1)
Burgess et al. 2008
Conlon, Maharana, FQ

27. Global Embedding and
Moduli Stabilisation
Cicoli, Krippendorf,Mayrhofer, FQ, Valandro

28. Global Picture

29. Classification from Toric
Ambient Spaces

30. Concrete (Compact) Calabi-Yau
ection we summarise the details of the CY manifold we already presented in [2]
or the following analysis. The toric ambient variety into which the CY hypersu
mbedded is given by the following weight matrix:
z1 z2 z3 z4 z5 z6 z7 z8 DeqX
1 1 1 0 3 3 0 0 9
0 0 0 1 0 1 0 0 2
0 0 0 0 1 1 0 1 3
0 0 0 0 1 0 1 0 2
,
10
tanley-Reisner ideal is
SR = {z4 z6, z4 z7, z5 z7, z5 z8, z6 z8, z1 z2 z3} . (18
the last column of the table indicates the degrees of the hypersurface equation
e Hodge numbers of the CY are h1,1
= 4 and h1,2
= 112, such that χ = −216
more, the three toric divisors D4, D7 and D8 are all P2
, or dP0, on X and mutuall
secting.
H1,1
(X) we chose the basis8
involution
orientifold involution that exchanges two of the three dP0 divi
iteria are met if we choose the following involution:
z4 ↔ z7 and z5 ↔ z6 ,
he CY hypersurface X symmetric under this holomorphic invo
t its complex structure such that the defining equation eqX = 0
nvolution. From (25) we see that the two dP0’s at z4 = 0 an
an orientifold involution that exchanges two of the three dP0 divisor
e criteria are met if we choose the following involution:
z4 ↔ z7 and z5 ↔ z6 ,
e the CY hypersurface X symmetric under this holomorphic involut
trict its complex structure such that the defining equation eqX = 0 is
e involution. From (25) we see that the two dP0’s at z4 = 0 and
nged by the involution. Furthermore, in [2] we showed that the inva
ven by the following two orientifold planes:
O7-planes Locus in ambient space Homology class in X3
O71 : y6 = z4z5 − z6z7 = 0 DO71 = D6 + D7 = Db
O72 : y5 = z8 = 0 DO72 = D8 = Ds
Orientifold

31. dP0 with only D3 Branes

32. Consistency Constraints
• Orientifolding induces orientifold
planes with non zero 3-7 charges
• D7 tadpoles ✔
• D5 tadpoles ✔
• D3 tadpoles ✔
• Freed-Witten anomaly ✔
• K-theory charges ✔

33. Moduli Stabilisation
Minkowski vacuum, Ms=MGUT~1016 GeV,
sequestered SUSY soft terms TeV (~1/V2).

34. Sequestered Scenario
* No CMP,
* No gravitino induced moduli problem,
* Volume reheating
Model independent !
MGUT~1016 GeV

35. dP0 D3 and Flavour D7 Branes
set of values of ni to a different set.
n2n0
n1
m1
m0m2
Figure 1: The dP0 quiver encoding the SU(n0) × SU(n1) × SU(n2) gauge theory with flavour branes.
Potential D7-D7 states are not shown.
2.2 Compact Models and constraints on local chargesfor flavour
branes
We now want to embed the local models on the dP0 singularity with D3 and flavour D7
ocus on the simplest models based on the Z3 singularity or r
o singularity dP0. The extended quiver diagram including flav
gure 6. Each node with label ni corresponds to a U(ni) gauge
bi-fundamental fields (ni, ¯nj). For each gauge group, a dist
The ni denote the multiplicity of each fractional brane leading
oup U(ni). Given a choice of D3 brane gauge groups ni, the fla
m0, m1, m2 are constrained by anomaly cancellation:
m0 = m + 3(n1 − n0) m1 = m m2 = m + 3(n1 − n2) .
ing the number of D3 branes n0, n1, n2 in order to look for a
e number of D7 branes up to a free integer m.2
ple, choosing all D3-brane gauge groups to equal three n0 =
Non-compact (local) case: m arbitrary
Compact (global embedding): m is highly constrained!
that the charge has to be a positive multiple of H.
gives strong constraints on the numbers ni, mi for the lo
compact CY manifold:
m ≥ 0 3(n1 − n0) + m ≥ 0 3(n1 − n2) + m ≥ 0 ,
to
0 ≤ −m ≤ 3(n1 − max{n0, n2}) .
e.g. n0=n1=n2 implies m=0!!!

36. A LR-Model: Brane Set-up
σ
π
φ
χ
+-χ
σ
-
+
+
φ-
dP'dP 00
D72
flav
D72
flav'
D70
flavD70
flav'
D7SU(2) D7SU(2)'
re 3. Brane setup: The red points represent the fractional branes. There are two branes

37. Moduli Stabilisation
4
(yellow line), W0 = 10−7
(purple line), W0 = 10−14
(green line);
this result into (3.34), we find
V =
W2
0
V3
3ζ
4g
3/2
s
−
3
2
ln (V/W0)
as
3/2
+ p
V1/3
[ln (V/W0)]2 .
ng with respect to V we obtain
=
3
2
ln (V/W0)
as
3/2
1 −
1
2 ln (V/W0)
−
8
9
p
V1/3
[ln (V/W0)]2 1 +
3
4 ln (V/W
bstituted in (3.36) yields the following expression for the vacuum energy
V =
W2
0
V 3
ln
V
W0
−
3
4 a
3/2
s
+
p
9
V 1/3
[ln (V/W0)]5/2
1 −
6
ln (V/W0)
.
= π/3 and writing V = 10x, Figure 4 shows how the vacuum energy chan
W0 = 10 (yellow line), W0 = 10 (purple line), W0 = 10 (green line);
Plugging this result into (3.34), we find
V =
W2
0
V3
3ζ
4g
3/2
s
−
3
2
ln (V/W0)
as
3/2
+ p
V1/3
[ln (V/W0)]2 . (3
Minimising with respect to V we obtain
3ζ
4g
3/2
s
=
3
2
ln (V/W0)
as
3/2
1 −
1
2 ln (V/W0)
−
8
9
p
V1/3
[ln (V/W0)]2 1 +
3
4 ln (V/W0)
(3
which substituted in (3.36) yields the following expression for the vacuum energy
Λ ≡ V =
W2
0
V 3
ln
V
W0
−
3
4 a
3/2
s
+
p
9
V 1/3
[ln (V/W0)]5/2
1 −
6
ln (V/W0)
. (3
Setting as = π/3 and writing V = 10x, Figure 4 shows how the vacuum energy changes
function of x for different values of W0 at constant p (shown here for cσ = 1 and cφ = 1
The preferred values of V and W0 are chosen in such a way to obtain a Minkow
vacuum and TeV-scale supersymmetry at the same time. In the presence of flavour bra
Plugging this result into (3.34), we find
V =
W2
0
V3
3ζ
4g
3/2
s
−
3
2
ln (V/W0)
as
3/2
+ p
V1/3
[ln (V/W0)]2 .
Minimising with respect to V we obtain
3ζ
4g
3/2
s
=
3
2
ln (V/W0)
as
3/2
1 −
1
2 ln (V/W0)
−
8
9
p
V1/3
[ln (V/W0)]2 1 +
3
4 ln (V/W
which substituted in (3.36) yields the following expression for the vacuum energy
Λ ≡ V =
W2
0
V 3
ln
V
W0
−
3
4 a
3/2
s
+
p
9
V 1/3
[ln (V/W0)]5/2
1 −
6
ln (V/W0)
.
Setting as = π/3 and writing V = 10x, Figure 4 shows how the vacuum energy chan
unction of x for different values of W0 at constant p (shown here for cσ = 1 and cφ
The preferred values of V and W0 are chosen in such a way to obtain a Mi
vacuum and TeV-scale supersymmetry at the same time. In the presence of flavour
oop corrections to the visible sector gauge kinetic function might induce moduli
Two flux ‘parameters’: gs=1/65, W0=0.01
Determine 4 physical quantities:
Ms=1012 GeV, 1α = 20, Λ~0, Msoft~TeV
(But CMP?).

38. Unification
MZ Mbreaking MString
Α3
1
Α2
1
Αy
1
10 1000 105 107
109
1011
1013
x GeV
20
40
60
80
100
Α 1

39. Web of Quiver Models

40. Quiver Transitions
until it splits into a brane wrapping (1+αb
)Db −Dq1 and one wrapping Dq1 ; if this last brane
has the suitable flux such that its charge vector is minus the charge vector of one of the
fractional branes, then it annihilates with it, lowering the corresponding multiplicity ni. As
we can already see from the D7-charge, the only fractional branes that can be annihilated
are F0 and F2 because they have the charge of an anti-D7-brane wrapping Dq1 .
3
33
3
23
1
Figure 3: Transition from the SU(3)3
quiver to the SU(3)2
× SU(2): One D7-brane (solid green line)
on top of the O-plane (dotted line) splits into a flavour brane intersecting the fractional branes (red and
blue lines) and into an anti-fractional brane. This last one annihilates one fractional brane from the red

41. Transitions continuuing
3
33
3
11
2 2
...
Figure 4: By repeating four times the transition described in Figure 3, we get four flavour branes and no
D7-brane on top of the O-plane.

42. Web of Quiver Models

43. CONCLUSIONS
• Continuous progress on local string
models
• Several SUSY breaking scenarios
• Local models: Global embedding and
Moduli Stabilisation!!!
ü Most local models not global embedding
ü Those that have form a web
• Most known ingredients used: geometry,
fluxes, branes, perturbative, non-perturbative effects
• Many open questions

44. ICTP
Trieste, Italy
August 26-31 2013
susy2013.ictp.it

45. Dark Radiation
Energy density:
At CMB: WMAP, ACT, SPT
Standard Model Neff=3.04

46. Volume Reheating
Volume axion ab
Closed string axions
Higgses
Matter scalars C
Simplest:
General: Strong constraints on
matter and couplings!

47. SM Cycle does not break SUSY!
‘Fayet-Iliopoulos’ à0
‘Sequestered moduli/gravity mediated SUSY Breaking’
No-scale (vanishing soft terms) Suppressed !

48. Sequestered Scenario
* No CMP,
* No gravitino induced moduli problem,
* Volume reheating
Model independent !
MGUT~1016 GeV

49. Higher del Pezzos
Triplication of families very limited
In general most quivers k<4 arrows
For dP8 model, see
H.Verlinde, M.Wijnholt (+Buican, Malyshev, Morrison) 06,07

50. ‘Realistic’ ‘Pati-Salam’
Model (dP3)
• Break symmetry to SM (+ U(1) or LR)
• Breaking U(1) to SM: RH sneutrino
(R-parity broken)
• Quark+ lepton mass hierarchies
• See-saw neutrino masses
• Stable proton
• CKM, CP
• Controlled kinetic terms!! !!!
• Gauge Unification

51. 3
33
1
22
3
2
2
2
2
2
2
1
1
22
3