[PPT] - The F-ate of GUTs Sakura Sch afer-Nameki Seminar at DAMTP, PowerPoint Presentation

SLIDE 1

The F-ate of GUTs

Sakura Sch¨ afer-Nameki Seminar at DAMTP, Cambridge, March 3, 2011 Joe Marsano, Natalia Saulina, SS-N

0808.1286, 0808.1571, 0808.2450, 0904.3932, 0906.4672, 0912.0272, 1006.0483, WIP2

and with Matt Dolan 1102.0290, WIP

SLIDE 2

Two Key Questions in String Phenomenology

Is there any realistic particle physics within string theory? Is there an imprint of the UV completion(s) upon the low energy physics?

SLIDE 3

Three-Step Strategy

Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s MGUT

MPl ∼ 10−3:

SU(5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc.

[Aldazabal, Ibanez, Quevedo, Uranga]

SLIDE 4

Three-Step Strategy

Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s MGUT

MPl ∼ 10−3:

SU(5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc. Is there an imprint of the UV completion(s) upon the low energy physics? Step 2: Global consistency and embeddability

⇒ Constraints on low energy theory ⇒ Impact on: spectrum, flavour structure

SLIDE 5

Three-Step Strategy

Is there any realistic particle physics within string theory? Step 1: Low energy gauge dof’s decoupling gravity dof’s MGUT

MPl ∼ 10−3:

SU(5) SUSY GUT, SUSY-breaking, flavour, neutrino physics, etc. Is there an imprint of the UV completion(s) upon the low energy physics? Step 2: Global consistency and embeddability

⇒ Constraints on low energy theory ⇒ Impact on: spectrum, flavour structure

Step 3: Construction of full-fledged string compactifications

Algebraic geometry gymnastics
Moduli stabilization

SLIDE 6

Three-Step Strategy with F-theory

Step 1. Ultra-local Models:

⇒ Effective field theory on 7-branes: SU(5) GUT

Step 2. Semi-local Model: Impose general conditions for embedding into local CY4

⇒ Embeddability implies strong phenomenological restrictions

Step 3. Global Model: Construction of elliptically fibered CY4 realizing semi-local models

SLIDE 7

Bottom-up Three-Step Strategy

Step 3: Step 2: Step 1: Global Model: Semi-local Model: Local Model: Compact Geometry + Fluxes Embeddability

⇒ strong pheno

restrictions Effective field theory

n D-branes:

SU(5) GUT

SLIDE 8

Why care? LHC is excluding more and more of the CMSSM parameter space

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.5 1.0 1.5 2.0 2.5 M1 2 Μ m

0 Μ

CMSSM pa ra m e te r spa cewithta nΒ 3, A0

10 100 1000 30 300 3000 na tura lne ssproba bility gluinom a ssinGe V e xclude dby LEP e xclude dby LHC a llowe d

Strumia 1101.2195 NB: there is a tiny white sliver of allowed parameter space.

SLIDE 9

References

Step 1. Ultra-local Models:

[Donagi, Wijnholt], [Beasley, Heckman, Vafa]: GUTs [Marsano, Saulina, SS-N ], [Heckman, Marsano, Saulina, SS-N, Vafa]: SUSY-breaking [Heckman, Vafa + Bouchard, Cecotti, Cheng, Seo, Tavanfar,... ], [Watari, Tatar + Hayashi, Kawano, Toda, Tsuchiya, Yamazaki]: : Cosmology, Neutrinos, Flavour.

Step 2. Semi-local Model:

[Hayashi, Kawano, Tatar, Watari], [Donagi, Wijnholt]: spectral cover [Marsano, Saulina, SS-N]: spectral cover, phenomenological constraints from semi-local models

Step 3. Global Model:

[Marsano, Saulina, SS-N]: compact geometry for F-theory GUTs [Blumenhagen, Grimm, Jurke, Weigand], [Cordova]: other examples

SLIDE 10

Outline

0. Bottom-up: Local, semi-local, global
1. Local F-theory GUTs
2. Constraints: anomaly cancellation and Dudas-Palti relations
3. Semi-local and Global Model
Embedding into local E8 singularity
Monodromies
Global geometry
Survey
4. Phenomenological Implications
Gauge-mediation with non-GUT messenger sector
5. Conclusions and Outlook

SLIDE 11

1. Local Models

Low energy gauge dof’s decoupling gravity dof’s MGUT

MPl ∼ 10−3:

SU(5) SUSY GUT

3 generations of

10M =     Q ∼ (3,2)+1/6 Uc ∼ (¯ 3,1)−2/3 Ec ∼ (1,1)+1     , ¯ 5M = Dc ∼ (¯ 3,1)+1/3 L ∼ (1,2)−1/2

Higgses: lifting triplets

5H = Hu ∼ (1,2)+1/2 H(3)

u ∼ (3,1)−1/3

,

¯ 5H = Hd ∼ (1,2)−1/2 H(3)

d ∼ (¯

3,1)+1/3

W ∼ λu 5H × 10M × 10M + λd ¯

5H × ¯ 5M × 10M

SUSY-breaking, flavour, neutrino physics, etc.

SLIDE 12

MSSM from Brane-intersections

Gauge dof’s from worldvolume
Matter from Brane-intersections or

equivalently: Higgsing a higher rank group by adjoint vevs φa: G → SU(5) × U(1)

MSSM interactions

W ∼ λu 5H × 10M × 10M

+λd ¯

5H × ¯ 5M × 10M

⇒ Can get all these from Higgsing G → SU(5) × U(1)k as long as G ⊃ E7 ⇒ Non-perturbative string theory

SLIDE 13

F-theory

F-theory [Vafa][Morrison, Vafa] =Type IIB [Green, Schwarz] vacua with varying axio-dilaton:

τ = C0 + ie−φ

Geometrize τ consistent with SL2Z

⇒ compactify to d = 4 on elliptically fibered CY4 with base B6:

Eτ → X4

↓

B ⊃ S

SLIDE 14

Gauge degrees of freedom/D-branes in F-theory

F-theory: realizes (stacks of) branes in terms of geometric singularities Singularity type: An: y2 = x2 + zn+1 Dn: y2 = x2z + zn−1 E6: y2 = x3 + z4 Perturbative interpretation: An: IIB with D7-branes Dn: IIB orientifolded with D7 and O-planes En: no perturbative IIB picture, ”exceptional 7-branes”

SLIDE 15

Matter fields

[BHV I, II], [Donagi, Wijnholt]

7-branes inside B6 wrapping surfaces, which intersect over a curve Σ:

= ⇒ ⇒

Bifundamental matter is localized along curves Σ

⇒

GΣ → SU(5) × U(1), in particular: SU(6) : 5, ¯ 5, SO(10) : 10,10

⇒

Chiral matter from additional gauge fluxes

SLIDE 16

Example: SU(6) enhancement

Simplest case: Switching on a single deformation on A5 singularity y2 = x2 + z6

→

y2 = x2 + (z − λ)z5 corresponds to breaking SU(6) → SU(5) × U(1). From the point of view of local enhancements: G1 = SU(5), G2 = U(1): GΣ = SU(6)

→

SU(5) × U(1) 35

→

240 ⊕ 10 ⊕ 56 ⊕ 5−6 Adjoints Bifundamentals 5 ⊕ 5 are the bifundamental matter fields localized at Σ.

SLIDE 17

Yukawa couplings from Triple-Intersections

[BHV I, II], [Donagi, Wijnholt]

Yukawa couplings from triple intersection of matter curves: Gp → SU(5) × U(1)1 × U(1)2 Such as SO(12) : ¯ 5H × ¯ 5M × 10M E6 : 10M × 10M × 5H SU(7) : 5 × ¯ 5 × 1

SLIDE 18

SU(5) F-theory GUT

[BHV II]

SO(10)

SU(5)

SU(6) E6 SO(12)

⇒ W ∼λb

ij ¯

H5Φi

5Φj 10 + λt ij H5Φi 10Φj 10 ⇒ QDHd + LEHd + QUHu

SLIDE 19

GUT breaking

[BHV I, II], [Donagi, Wijnholt]

GUT-breaking by hypercharge flux FY: SU(5) → SU(3) × SU(2) × U(1)Y 24 → (8,1)0 ⊕ (1,3)0 ⊕ (1,1)0 ⊕ (3,2)−5 ⊕ (3,2)+5 Gauge Fields Exotics FY lifts XY and solves doublet-triplet splitting: FY|ΣM = 0, FY|Σ5H = +1, FY|Σ5H = −1 Masslessness of U(1)Y: imposes topological condition

[Buican, Malyshev, Morrison, Verlinde, Wijnholt]

⇒ FY is dual in SGUT to 2-cycle, that is homologically trivial in B

SGUT

Ω3

e2 e1

SLIDE 20

Summary of Step 1: Local model

⇒ Geometric engineering of SU(5) GUT ⇒ GUT breaking using hypercharge flux FY ⇒ ”anything goes”, realistic SU(5) GUTs, SUSY breaking, etc. [Marsano,

Saulina, SSN], [Heckman, Vafa]

⇒ Absence of dim 5 proton decay and µ-term: additional U(1)s

U(1)PQ : qPQ(Hu) + qPQ(Hd) = 0 For instance:

10M ¯ 5M 5H ¯ 5H U(1)PQ

−1 −1

2 2

⇒ Absence of tree-level:

W ∼ µHuHd and Wdim5 ∼ 1 Λ Q3L Summary: Local models allow lots of model building freedom

SLIDE 21

2. Constraints: Anomaly cancellation

All phenomenologically viable local F-theory GUTs have additional U(1)’s (protection from proton decay, µ-term). Sources of additional constraints:

Cancellation of mixed MSSM and U(1) anomalies
Embedding into (local) CY4 geometry

GUT-breaking by hypercharge

⇒ U(1)Y masslessness ensured by topological condition on FY ⇒ FY cannot introduce any additional gauge anomalies

However:

⇒ FY restriction on Σ10 and Σ¯

5 generates chiral spectrum

⇒ Require G2

MSSM × U(1) mixed anomaly cancellation for additional U(1)

SLIDE 22

Dudas-Palti Relations

G2

MSSM × U(1) mixed anomaly cancellation for additional U(1) imply

[Dudas, Palti][Marsano][Dolan, Marsano, Saulina, SSN]

∑

10 matter curves,Σi

10

qi

Z

Σ(i)

10

FY =

∑

5 matter curves, Σa

5

qa

Z

Σ(a)

5

FY Consequences of these Dudas-Palti relations:

Minimal SU(5) GUT

⇒ the only U(1) compatible is U(1)χ (B − L and Y)

If there is a U(1)PQ

⇒ there are always non-GUT exotics

SLIDE 23

Consequence 1: Uniqueness of U(1)χ

Question: minimal SU(5) GUT with U(1). What U(1)s are possible? GUT breaking and absence of exotics requires that FY restricts as:

Z

ΣHu

FY = +1,

Z

ΣHd

FY = −1,

Z

ther Σ′ FY = 0

DP relations/anomaly cancellation

∑

10 matter curves,Σi

10

qi

Z

Σ(i)

10

FY =

∑

5 matter curves, Σa

5

qa

Z

Σ(a)

5

FY

⇒

qHu + qHd = 0 The only possible U(1) compatible with MSSM interactions and SU(5)

[Marsano, Saulina, SSN] 10M ¯ 5M 5H ¯ 5H U(1)χ

−1

3 2

−2

But U(1)χ does not forbid Wdim 5!

SLIDE 24

Consequence 2: Absence of proton decay implies Exotics

Phenomenologically we require absence of: W ∼ µHuHd and Wdim5 ∼ 1 Λ Q3L Requires the U(1) to be a PQ symmetry, i.e. qHu + qHd = 0 U(1)PQ

⇒

non-GUT Exotics More precisely, these are vector-like pairs wrt MSSM gauge group:

∑

10 matter curves, i

Z

Σ(i)

10

FY = 0,

∑

5 matter curves, a

Z

Σ(a)

5

FY = 0 Can lift these by singlets X, with PQ-charge and vev Wex = λX fex ¯ fex

SLIDE 25

U(1) Symmetries and Exotics

[Dolan, Marsano, Saulina, SSN]

No µ and no dim 5 proton decay ⇒ U(1)PQ ⇒ By DP relations: non-GUT exotics

SU(5) origin Exotic Multiplet Degeneracy (1,1)+1 ⊕ (1,1)−1 M + N 10 ⊕ 10 (3,2)+1/6 ⊕ (3,2)−1/6 M (3,1)−2/3 ⊕ (3,1)+2/3 M − N 5 ⊕ 5 (3,1)+1/3 ⊕ (3,1)−1/3 K (1,2)−1/2 ⊕ (1,2)+1/2 K − L with M ≥ |N| K ≥ 0 K − L ≥ 0

In particular: the PQ-charges of the Higgses are: qHu + qHd = qX∆, ∆ ≡ N − L

⇒ Survey of all such models in F-theory

[Dolan, Marsano, Saulina, SSN]

SLIDE 26

Unification

[Dolan, Marsano, SSN] work in progress

Apart from consistency with anomalies (DP relations), phenomenological requirements (no dim 5 proton decay, µ-term), we need to ensure consistency with unification. Additional non-GUT exotics contribute to 1-loop β-functions as

δb1 = 3M + K + 1

5 (−2N − 3L)

δb2 = 3M + K − L δb3 = 3M − N + K .

In particular, non-universality is measured by qHu + qHd = qX∆, where ∆ = N − L = δb2 − δb3 = 1 6 (5δb1 + 3δb2 − 8δb3)

SLIDE 27

Unification versus Proton Decay

[Dolan, Marsano, SSN] work in progress

We parametrized the models by qHu + qHd = qX∆, where ∆ = N − L = δb2 − δb3 = 1 6 (5δb1 + 3δb2 − 8δb3)

Unification: ∆ measures disruption from unification
Proton decay: the following coupling is allowed

1 Λ

Z

d2θ X Λ ∆ Q3L

⇒ Intrinsic tension: Unification versus protection from Proton Decay ⇒ Requires analysis of RG contributions (high and low-scale thresholds)

SLIDE 28

Summary: Constraints from Anomalies and DP relations

Framework: SU(5) GUTs with FY GUT breaking and additional U(1)

Anomaly cancellations imply conditions on U(1) charges
Requiring minimal SU(5) ⇒ uniquely determines U(1) as U(1)χ

But phenomenologically this is not favorable!

Requiring no µ-term/dim 5 proton decay ⇒ U(1)PQ ⇒ Exotics
Tension between exotics and unification

⇒ ”Anything goes” in local models turns out to be too naive ⇒ Consistency requirements highly constrain phenomenology

SLIDE 29

3. Semi-local and Global Model

Impose constraints arising from embedding into local CY4: Global CY4: Local CY4: elliptic fibration over B ALE-fibration over SGUT y2 = x3 + f x + g Eτ → X4

↓

B ⊃ SGUT ALE → X4

↓

SGUT For SU(5) GUTs: Deformed E8 singularity over SGUT

SLIDE 30

E8 singularity over SGUT

Local geometry around F-theory 7-branes is a deformed E8 singularity

y2 = x3 + b5xy + b4x2z + b3yz2 + b2xz3 + b0z5

⇐ ⇒ E8 gauge theory broken to SU(5) by adjoint VEVs

SLIDE 31

Local E8 singularity over SGUT

y2 = x3 + b5xy + b4x2z + b3yz2 + b2xz3 + b0z5

E8 singularity: b2,3,4,5 = 0
SU(5) GUT:

SU(5) : bm = 0 SO(10): 10 matter 0 = b5 SU(6) : 5 matter 0 = P = b0b2

5 − b2b3b5 + b2 3b4

SO(12) : Bottom: 0 = b5 = b3 E6 : Top: 0 = b5 = b4

⇒ bm parametrize Higgs bundle that breaks E8 gauge theory to SU(5)

bm ∼ Trφmb0

SLIDE 32

Main idea

How do constraints from embedding into semi-local model to arise? E8 → SU(5)GUT × U(1)4 Higgsed by adjoint vevs φ = diag(λ1, λ2, λ3, λ4, λ5)

Naively (aka local model):

GUT-fields carry 4 independent U(1)s

Semi-local model:

λi vary over base and get identified by monodromies ⇒ U(1)’s get identified by monodromies

Geometry is specified in terms of bn: bn(λi) = b0 Pn(λi), Pn = symmetric polynomial

⇒ monodromies acting on roots λi(bn).

SLIDE 33

Geometric Models and DP relations

[Dolan, Marsano, Saulina, SS-N]

Elliptic fibrations (semi-local models) realizing n U(1) symmetries:

bm have to be tuned (complext structure)

Anomaly cancellation/Dudas-Palti relations:

Restriction on U(1) charge distributions

⇒ Survey of all consistent semi-local models ⇒ NB: requires also the study of fluxes (for chiral matter)

SLIDE 34

Survey

Parametrization of non-GUT exotics:

SU(5) origin Exotic Multiplet Degeneracy (1,1)+1 ⊕ (1,1)−1 M + N 10 ⊕ 10 (3,2)+1/6 ⊕ (3,2)−1/6 M (3,1)−2/3 ⊕ (3,1)+2/3 M − N 5 ⊕ 5 (3,1)+1/3 ⊕ (3,1)−1/3 K (1,2)−1/2 ⊕ (1,2)+1/2 K − L

Then all semi-local models fall into the following classification:

Model Class Exotic Spectra Dim 5 I N − L = 1 XQ3L/Λ2 II N − L = 2 K ≥ M X2Q3L/Λ3 III L = 2 M = N = 0 X†2Q3L/Λ4 IV N − L = 1 K − L = M XQ3L/Λ2

SLIDE 35

Comments:

Model Class Exotic Spectra Dim 5 I N − L = 1 XQ3L/Λ2 II N − L = 2 K ≥ M X2Q3L/Λ3 III L = 2 M = N = 0 X†2Q3L/Λ4 IV N − L = 1 K − L = M XQ3L/Λ2

Analysis of unification requires N − L < 0 ⇒ Model III
We surveyed all semi-local models:

⇒ survey does not require specification of geometry ⇒ realized in 3-fold base

[Marsano, Saulina, SS-N]

⇒ Lift to global model from semi-local model.

Global description of fluxes (G-fluxes)

[Marsano, Saulina, SS-N]

Is non-universality prominent enough to distinguish these from

universal ones?

SLIDE 36

Side-Remark: A Geometry for a Global Model

[Marsano, Saulina, SS-N]

Explicit realization in compact CY4: ”Proof of principle” Recall: X4 = elliptically fibered CY4 with three-fold base B: Eτ → X4

↓

B ⊃ SGUT Constraints on B6:

X4 Calabi-Yau: B almost Fano

i.e. K−1

B3 semi-ample

Hypercharge constraint: FY dual in SGUT to a

2-cycle that is trivial in B

SGUT

Ω3

e2 e1

Furthermore: G-fluxes in singular CY4

[Marsano, Saulina, SS-N]

SLIDE 37

Hypercharge flux constraint

[Buican, Malyshev, Morrison, Verlinde, Wijnholt] [Beasley, Heckman, Vafa], [Donagi, Wijnholt]

Let S = dPn and H2(dPn,Z) = h, e1,··· , en , h2 = 1, ei · ej = −δij Representative for hypercharge flux [FY] = e1 − e2 Hypercharge U(1)Y remains massless if there is a 3-chain Ω3 in B3:

∂Ω3 = e1 ∪ (−e2)

SGUT

Ω3

e2 e1

SLIDE 38

Three-Fold Construction

[Marsano, Saulina, SS-N]

C P3

G C p0 SGUT C G

1. Starting point:

nodal curve C, locally xy = z = 0

2. Blowup along C:

Conifold singularity xy = zu 3. Blowup conifold to SGUT = P1 × P1 P1’s homologous in 3-fold Local construction embeddable into the resulting 3-fold

SLIDE 39

4. F-enomenology

Semi-local F-theory GUTs with gauged U(1)PQ

⇒ automatically non-GUT exotics ⇒ this is generic: independent of the specifics of the CY4

Exotics arising from FY restricting non-trivially to 10 and ¯ 5 matter curves:

SU(5) origin Exotic Multiplet Degeneracy (1,1)+1 ⊕ (1,1)−1 M + N 10 ⊕ 10 (3,2)+1/6 ⊕ (3,2)−1/6 M (3,1)−2/3 ⊕ (3,1)+2/3 M − N 5 ⊕ 5 (3,1)+1/3 ⊕ (3,1)−1/3 K (1,2)−1/2 ⊕ (1,2)+1/2 K − L

SLIDE 40

What is the phenomenology of such models?

[Dolan, Marsano, SS-N] in progress

SUSY breaking and phenomenology of non-GUT exotics:

⇒ non-GUT exotics as gauge messengers:

W ⊃ FXX + X f ¯ f

⇒ coupling from 10 × 10 × 1 ⊂ 2483

SLIDE 41

GMSB with non-GUT exotic Messengers

W = FXX + λXX f ¯ f + WSU(5)GUT Forbid µ-term and dim 4 proton decay at tree-level by U(1)PQ X 10M ¯ 5M 5H ¯ 5H U(1)PQ

−2

1

−1 −2

X picks up VEV, µ dynamically generated by 1 MGUT

Z

d4θX†HH

⇒ µ ∼

FX MGUT

⇒ FX ∼ 1019 GeV2, i.e. high-scale GMSB, Sweetspot SUSY/local F-theory

[Ibe, Kitano], [Marsano, Saulina, SSN])

SLIDE 42

GMSB gaugino masses: Mi

1/2(MMess) = δbi

αi(MMess) 4π

FX

MMess

2-loop squark and slepton masses:

m2

Q(MMess) =

∑

relevant i

ci δbi αi(µ)2 8π2

FX

MMess

2

Beta-function shifts from exotics:

δb1 = 3M − 2

5 N + K − 3 5 L

δb2 = 3M + K − L δb3 = 3M − N + K .

SLIDE 43

Gaugino Mass Relations

Standard universal gaugino mass relations M1 : M2 : M3 ≃ 1 : 2 : 6 gets replaced by M1 : M2 : M3 ≃ 1 : 2

3M + K − L

3M − 2N/5 + K − 3L/5

: 6
3M + K − N

3M + K − 2N/5 − 3L/5

Two benchmark flux choices:
Maximal deviation from universality: (K, L, M, N) = (0,0,1,1)
Large Flux, compatible with perturbativity: (K, L, M, N) = (20,6,9,7)

SLIDE 44

Parameter Scan: tanβ

Paramaters: (MMess, Λ = FX/MMess)

tanβ (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 15 20 25 30 35 40 45 tanβ (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 5 10 15 20 25 30 35 40 45

M = N = 1 M = 1, N = 0

SLIDE 45

Parameter Scan: Physical Higgs mass

mh (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 30 40 50 60 70 80 90 100 110 120 mh (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 85 90 95 100 105 110 115 120 125 130

M = N = 1 M = 1, N = 0 Consistency with LEP bound for Non-GUT exotic messengers: 104.5 < Λ < 105 GeV NB: for standard 5 ¯ 5 messengers, 105 < Λ < 106 GeV for the same MMess

SLIDE 46

Parameter Scans for large Flux

Paramaters: (MMess, Λ = FX/MMess) for K = 20, L = 6, M = 9, N = 7.

tanβ (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 15 20 25 30 35 40 45 mh (GeV) 3 3.5 4 4.5 5 5.5 6 log10(Λ (GeV)) 12 13 14 15 log10(Mmess (GeV)) 110 112 114 116 118 120 122 124 126 128 130

SLIDE 47

Comparison with mGMSB Lookalike

d

L

u

L s
L

c

L

d

R

u

R s
R

c

R

b

1

t

1

b

2 t
2

e

LΝ
e Μ
L Ν
Μ

Τ

1

Ν

Τ

e

R Μ
R

Τ

2

M1 M2 M3 Χ

1

Χ

2

Χ

3

Χ

4

Χ

1
Χ
2
200

400 600 800 1000 1200 1400 masses GeV

d

L

u

L s
Lc
L

d

Ru
R s
Rc
R

b

1

t

1

b

2 t
2

e

LΝ
e Μ
L Ν
Μ

Τ

1

Ν

Τ

e

R Μ
R

Τ

2

M1 M2 M3 Χ

1

Χ

2

Χ

3 Χ
4

Χ

1
Χ
2
200

400 600 800 1000 1200 1400 masses GeV

M = N = 1 M = 1, N = 0

SLIDE 48

Production Cross-Sections at LHC7

70000 80000 90000 100000 mg

GeV

0.1 1 10 Σfb Σg

q

Σ

t t

Σq

q

Σq

q

Σg

g

M = N = 1

SLIDE 49

40000 50000 60000 70000 80000 90000 100000 GeV 104 0.001 0.01 0.1 1 10 100 Σfb Σg

q

Σ

t t

Σq

q

Σq

q

Σg

g

M = 1

SLIDE 50

Gluino Branching Ratios

1000 1100 1200 1300 1400 mg

GeV

0.1 0.2 0.3 0.4 BR b

2b

b

1b

c

Rc

s

Rs

u

Ru

d

Rd

t

2t

t

1t

2000 4000 6000 8000 10000 mg

GeV

0.05 0.10 0.15 0.20 0.25 0.30 BR b

2b

b

1b

c

Rc

s

Rs

u

Ru

d

Rd

t

2t

t

1t

M = N = 1 M = 1, N = 0

SLIDE 51

Methods to distinguish from mGMSB Lookalike?

Models have very similar features (spectra, production cross sections,

large tanβ)

Distinction by RG invariants? [Carena, et al]
Reconstrution via [Allanach, Lester, Parker, Webber] by studying channels

˜ qL → χ0

2q → ˜

l±

R l∓q → χ0 1l±l∓q

Model mll medge

llq

mthr

llq

mhigh

lq

mlow

lq

MT2 mGMSB 194.2 894.3 452.9 720.4 727.8 22.4 F-GUT 295.8 905.4 492.9 723.5 761.9 22.0 mll = (m2

˜

χ1

0 − m2

˜

ℓR)(m2

˜

ℓR − m2

˜

χ2

0)/m2

˜

ℓR

= kinetic invariant for dilepton channel χ0

2 → ˜

l±l∓ → χ0

1l±l∓

SLIDE 52

5. So how are we doing...

”Life away from the brane is tough”... but more interesting, too.

Local model building was relatively flexible... but unpredictive
Anomaly cancellation constrains U(1) charges
Global embedding
Tension: U(1)PQ/Exotics/no-Proton-Decay versus Unification

⇒ F-theory GUTs become highly constrained (predictive?)

What assumptions did we make? GUT-breaking by hypercharge flux and U(1)s to prevent proton decay.

SLIDE 53

Outlook

How to get around the constraints:

Different GUT breaking mechanims? Wilson lines?
Discrete symmetries instead of U(1)s?

⇒ Unattractive

Given the framework we developed:

Pheno Signatures of Non-GUT exotics

⇒ This is precisely the kind of imprint of the UV-completion

Unification
Moduli stabilization

SUSY breaking: GMSB ok, or Gravity Mediation relevant?

Classification of Threefolds for F-theory CY4

SLIDE 54

.

SLIDE 55

A Geometry for a Global Model

[Marsano, Saulina, SS-N]

Explicit realization in compact CY4: ”Proof of principle” Recall: X4 = elliptically fibered CY4 with three-fold base B: Eτ → X4

↓

B ⊃ SGUT Constraints on B6:

X4 Calabi-Yau: B almost Fano

i.e. K−1

B3 semi-ample

Hypercharge constraint: FY dual in SGUT to a

2-cycle that is trivial in B

SGUT

Ω3

e2 e1

Furthermore: G-fluxes in singular CY4

[Marsano, Saulina, SS-N]

SLIDE 56

Hypercharge flux constraint

[Buican, Malyshev, Morrison, Verlinde, Wijnholt] [Beasley, Heckman, Vafa], [Donagi, Wijnholt]

Let S = dPn and H2(dPn,Z) = h, e1,··· , en , h2 = 1, ei · ej = −δij Representative for hypercharge flux [FY] = e1 − e2 Hypercharge U(1)Y remains massless if there is a 3-chain Ω3 in B3:

∂Ω3 = e1 ∪ (−e2)

SGUT

Ω3

e2 e1

SLIDE 57

Three-Fold Construction

[Marsano, Saulina, SS-N]

C P3

G C p0 SGUT C G

1. Starting point:

nodal curve C, locally xy = z = 0

2. Blowup along C:

Conifold singularity xy = zu 3. Blowup conifold to SGUT = P1 × P1 P1’s homologous in 3-fold Local construction embeddable into P3. B3 automatically Fano.

SLIDE 58

Exceptional divisor SGUT = P1

(1) × P1 (2) has required properties of SGUT:

P1

(1) ∼ P1 (2)

in H2(B3,Z) NB: Flopping the curve G yields dP2 divisor with same property. Divisors: H = dP3, D = F4 , E = SGUT = dP2 Final 3-fold: All holomorphic sections explicitly constructed

[Marsano, Saulina, SS-N]

S

GUT

H−D−E

D

e2 h−e1 h−e2 e1 h−e1−e2

SLIDE 59

Blank

SLIDE 60

On gauge-coupling unification in F-theory GUTs

[Donagi, Wijnholt], [Blumenhagen], [Conlon], [Dolan, Marsano, SS-N]

Running of gauge-couplings

α−1

i (mZ) = α−1 U + bi

2π ln MU mZ

+ δi

Additional corrections δi:

High-loop corrections (2-loop)
Low-scale thresholds: sparticles kick in only from their mass on
High scale thresholds: KK- modes (compactification dependent)
Exotics

Upshot: there is a range for the mass of the exotics such that consistency with measured gauge couplings is intact.

SLIDE 61

On gauge-coupling unification in F-theory GUTs

[Donagi, Wijnholt], [Blumenhagen], [Conlon], [Dolan, Marsano, SS-N]

Important scales in the problem: mz

→

MExotics

→

MKK

→

MWinding Scales in the compactification: RS, RB

M∗ = M∗(MPl, RB) measures 7-brane tension
M4

KK = αGUTM4

∗

R⊥ = R⊥(RS, RB) = size of direction transverse to SGUT
MWinding = R⊥M2

∗

SLIDE 62

MSSM-running:

With β1 = 3, β2 = −1, β3 = − 33

5

α−1

i (MGUT) = α−1 i (mz) − βi

2π ln MKK mz

KK-thresholds:

[Wijnholt ’10, private conversation]

– 8d theory 7-brane worldvolume theory has divergence from bulk – External contribution (from bulk) to cancel log divergence: divergence is capped off at winding scale [Conlon] MWinding = Winding scale > MKK Can be written in a 4d looking way

α−1

i

→ α−1

i

− βKK

2π ln MWinding MKK

SLIDE 63

Non-GUT exotic contribution:

α−1

i

→ α−1

i

− βExotics

2π ln MKK MExotics

δβ(exotic)

1

= 3M − 2N

5 + K − 3L 5

δβ(exotic)

2

= 3M + K − L δβ(exotic)

3

= 3M − N + K

In summary:

α−1

i

= α−1

i (mz) − βi

2π ln MKK mz

− βKK

2π ln MWinding MKK

− βExotics

2π ln MKK MExotics