mssm-like models from string theory · fabian ruehle (desy) mssm-like models from string theory...

MSSM-like models from String Theory

Fabian Ruehle

Deutsches Elektronensynchrotron DESYHamburg

Theory Seminar at University of Liverpool02/12/2014

Based on: [1401.5084]

Motivation

Motivation

Starting point: Description of fundamental forces� Standard Model (SM) describes strong, weak, and EM

interactions� General Relativity describes gravity� Both fit the data and observations extremely well

Reasons to go beyond� Lack a unified theory (quantum theory of gravity)� Explanations of hierarchies

I Radiative corrections to Higgs massI Why is gravity so much weaker than the other forces

� Need explanation for dark matter / dark energy� Hints for gauge coupling unification

Fabian Ruehle (DESY) MSSM-like models from String Theory Liverpool (02/12/2014) 1

Motivation

Motivation



Reasons to go beyond� Lack a unified theory (quantum theory of gravity)

� Explanations of hierarchiesI Radiative corrections to Higgs massI Why is gravity so much weaker than the other forces



Motivation

Motivation







Motivation

Motivation





� Need explanation for dark matter / dark energy

� Hints for gauge coupling unification


Motivation

Motivation







Motivation

Motivation

Solution approaches put forward� Supersymmetry� Extra dimensions� Grand Unified Theories (GUTs) like SU(5), SO(10), . . .

Theory including all these approachesString theory5 different string theories known: Type I, 2×Type II, 2×Heterotic

What is string theory� Replace point particles by extended 1D objects (strings)� Necessitates 10 dimensions� Naturally includes SUSY in 10D� 3/5 string theories naturally include GUT groups


Motivation

Motivation

A gift and a curseNeed to explain� Why do we see only 4 dimensions� Breaking of GUT groups� Breaking of SUSY without destabilizing hierarchy

Differences and similarities between the string theories� Both contain 10D SUSY� Both need to hide (compactify) 6 extra dimensions in a

specific way to keep low energy SUSY� Type I + Heterotic naturally include GUTs,

cosmology problematic� Type II better suited to discuss cosmology,

GUTs problematic


Motivation

Motivation



specific way to keep low energy SUSY

� Type I + Heterotic naturally include GUTs,cosmology problematic

� Type II better suited to discuss cosmology,GUTs problematic


Motivation

Motivation



specific way to keep low energy SUSY� Type I + Heterotic naturally include GUTs,

cosmology problematic� Type II better suited to discuss cosmology,

GUTs problematic


Motivation

Motivation

Pictorial illustration

Calabi–Yaus� Complicated geometrical objects to keep low-energy SUSY� Important quantities (e.g. metric) unknown� Have to rely on mathematical tools (topology, algebraic

geometry) for computations


Motivation

MotivationWhich of the five theories should we use?� All theories seem to be connected by dualities� There seems to be a theory (M-/F-Theory) which contains

all 5 string theories as limiting cases [Witten;Vafa]

� This connection requires interpolating through (poorlyunderstood) non-perturbative regimes

Idea of F-theory

� Introduce extra torus whose (varying) shape parameterdescribes coupling strength

� Take special limit where torus becomes singular ⇔ weaklycoupled regime to connect to other string theoriescompactified to 4D on 6D CY.

� Overall 12D theory with 8D Calabi–Yau (the torus plus other6D compactification)


Motivation




Idea of F-theory� Introduce extra torus whose (varying) shape parameter

describes coupling strength

� Take special limit where torus becomes singular ⇔ weaklycoupled regime to connect to other string theoriescompactified to 4D on 6D CY.



Motivation




Idea of F-theory� Introduce extra torus whose (varying) shape parameter

describes coupling strength� Take special limit where torus becomes singular ⇔ weakly

coupled regime to connect to other string theoriescompactified to 4D on 6D CY.



Motivation

Motivation


Calabi–Yaus� 4D hypersurfaces above which torus pinches correspond to

gauge groups

� Matter sits at 2D curves inside 4D surfaces� Yukawa couplings at points where 3 matter curves intersect


Motivation

Motivation



gauge groups� Matter sits at 2D curves inside 4D surfaces

� Yukawa couplings at points where 3 matter curves intersect


Motivation

Motivation



gauge groups� Matter sits at 2D curves inside 4D surfaces� Yukawa couplings at points where 3 matter curves intersect


Motivation

Outline

1 Motivation & introduction to F-Theory

2 Constraints on models from F-Theory + phenomenology

3 Model searches

4 Conclusion and outlook


Constraints on models

Motivation Constraints on models Model searches Conclusion

Wish list

Wish list for our modelsWant to . . .

1 . . . obtain SU(3)× SU(2)× U(1)Y GG of Standard Model(but allow for up to two extra abelian symmetries brokenat high scale)

2 . . . solve the GUT doublet-triplet splitting problem3 . . . get three families, one Higgs pair, no exotics

(but allow for extra massive singlets)4 . . . ensure absence of all quantum-anomalies5 . . . get realistic Yukawas (using extra singlets) [Froggatt,Nielsen]

6 . . . suppress proton decay operators (using extra symmetries)7 . . . suppress µ-term with extra “PQ symmetry” [Peccei,Quinn]



Wish list



2 . . . solve the GUT doublet-triplet splitting problem

3 . . . get three families, one Higgs pair, no exotics(but allow for extra massive singlets)

4 . . . ensure absence of all quantum-anomalies5 . . . get realistic Yukawas (using extra singlets) [Froggatt,Nielsen]




Wish list




(but allow for extra massive singlets)

4 . . . ensure absence of all quantum-anomalies5 . . . get realistic Yukawas (using extra singlets) [Froggatt,Nielsen]




Wish list




(but allow for extra massive singlets)4 . . . ensure absence of all quantum-anomalies

5 . . . get realistic Yukawas (using extra singlets) [Froggatt,Nielsen]




Wish list








Wish list





6 . . . suppress proton decay operators (using extra symmetries)

7 . . . suppress µ-term with extra “PQ symmetry” [Peccei,Quinn]



Wish list








F-Theory realization

Gauge group, doublet-triplet splitting, extra abelian symmetries� Start with 8D CY

� Find torus pinching such that there is a GUT SU(5)hypersurface S

� Do doublet-triplet splitting via hypercharge flux (VEV offieldstrength U(1)Y ⊂ SU(5))⇒ This VEV corresponds to a cycle which has to be trivial inthe 8D CY but non-trivial on S to not break U(1)Y symmetry[Beasley,Heckman,Vafa;Blumenhagen,Braun,Grimm,Weigand;Donagi,Wijnholt]

� Extra U(1) symmetries arise from further symmetryproperties of the torus⇒ This part is mathematically very challenging[Morrison,Park,Vafa,. . . ]




Gauge group, doublet-triplet splitting, extra abelian symmetries� Start with 8D CY� Find torus pinching such that there is a GUT SU(5)

hypersurface S

� Do doublet-triplet splitting via hypercharge flux (VEV offieldstrength U(1)Y ⊂ SU(5))⇒ This VEV corresponds to a cycle which has to be trivial inthe 8D CY but non-trivial on S to not break U(1)Y symmetry[Beasley,Heckman,Vafa;Blumenhagen,Braun,Grimm,Weigand;Donagi,Wijnholt]





Gauge group, doublet-triplet splitting, extra abelian symmetries� Start with 8D CY� Find torus pinching such that there is a GUT SU(5)

hypersurface S� Do doublet-triplet splitting via hypercharge flux (VEV of

fieldstrength U(1)Y ⊂ SU(5))⇒ This VEV corresponds to a cycle which has to be trivial inthe 8D CY but non-trivial on S to not break U(1)Y symmetry[Beasley,Heckman,Vafa;Blumenhagen,Braun,Grimm,Weigand;Donagi,Wijnholt]





Three families, one Higgs pair, no exotics� Within the GUT surface S we find matter curves:

I up to five 10-curves, 10→ (3, 2)1/6 + (3, 1)−2/3 + (1, 1)1I up ten 5-curves, 5→ (3, 1)1/3 + (1, 2)−1/2I up to 24 1-curves, 1→ (1, 1)0

� Each curve can give rise to (0,1,2,. . . ) particles⇒ Exact number depends on fluxes (field strengths) of other

symmetries in the theory� Each particle in addition charged under extra U(1)s� Some particles removed from theory by flux� Flux has to be s.t. quantum anomalies are absent

[Dudas,Palti;Marsano;Palti]







symmetries in the theory

� Each particle in addition charged under extra U(1)s� Some particles removed from theory by flux� Flux has to be s.t. quantum anomalies are absent








symmetries in the theory� Each particle in addition charged under extra U(1)s

� Some particles removed from theory by flux� Flux has to be s.t. quantum anomalies are absent








symmetries in the theory� Each particle in addition charged under extra U(1)s� Some particles removed from theory by flux

� Flux has to be s.t. quantum anomalies are absent[Dudas,Palti;Marsano;Palti]







symmetries in the theory� Each particle in addition charged under extra U(1)s� Some particles removed from theory by flux� Flux has to be s.t. quantum anomalies are absent




F-Theory realizationFlux parameterization and multiplicities

Σ10a : (3, 2)1/6: Ma Σ5i: (3, 1)1/3: Mi

(3, 1)−2/3 : Ma − Na (1, 2)−1/2: Mi + Ni(1, 1)1 : Ma + Na

Flux constraints from anomaly cancellation w/ SM factors∑i Mi −

∑a Ma = 0 ,

∑i Ni = 0 =

∑a Na

Flux constraints from anomaly cancellation w/ extra U(1) factors�

∑i qαi Ni +

∑a qαa Na = 0 ∀α

�∑

i qαi qβi Ni + 3∑

a qαa qβa Na = 0 ∀α, β

The last equation is not ensured by geometry and very restrictive!However, in the type II limit it has been argued that such ananomaly could be ok [Mayrhofer,Palti,Weigand]




Realistic Yukawas, suppress proton decay, suppress µ-term� Want one up-type Yukawa allowed at tree level (heavy top)� Want other Yukawas to be generated by singlet VEVs but

suppressed� Want all proton decay operators and µ-term to be

forbidden/sufficiently suppressed

ExampleQt ,Qu, t: (101)1,5 , u: (102)4,0 ,

Hu: (5Hu )−2,−10 , S1: (11)5,5

� Yukawas: QttHu, S1QuuHu� Up quark mass suppressed by 〈S1〉/Λ ∼ 10−2.. 10−3

� U(1)2 partially broken


Model searches


Previous approaches

Insist on exact MSSM spectrumThe only flavor-blind U(1) is U(1)B−L + U(1)Y , which allows forµ-term and dim 5 proton decay [Marsano,Saulina,Schafer-Nameki]

Insist on U(1) suppression of proton decay + µ-termµ-term only forbidden by PQ-symmetry, which lead tovector-like exotics of the SM GG and come in splitrepresentations of SU(5) [Dudas,Palti]

Possible way outAllow split representations for all 5-curves



Constraints I – Model limitations

Man-made constraints� Consider models with up to two additional U(1)s� Consider models without a priori present discrete Abelian

symmetries� Consider models where all 10-curves have the same U(1)

charges

U(1) charge patternq5 = Q5 + 5Z , q10 = Q10 + 5Z , q1 = 0 + 5Z

Charge offset M1 M2 M3 M4 M5Q5 0 1 2 3 4Q10 0 3 1 4 2

Analyzed by [Braun,Grimm,Keitel; Morrison,Park; Cvetic,Grassi,Klevers,Piragua;Borchmann,Mayrhofer,Palti,Weigand;. . . ]



Constraints II – Spectrum and anomaliesΣ10a : (3, 2)1/6: Ma Σ5i

: (3, 1)1/3: Mi(3, 1)−2/3 Ma − Na (1, 2)−1/2: Mi + Ni(1, 1)1 Ma + Na

Three chiral families + no anmoalies∑Ma =

∑M i = 3 with Ma,M i ≥ 0

⇒ Anomaly constraint∑

Ma −∑

M i = 0 satisfied

No exotics + no anmoalies∑Na = 0 with −Ma ≤ Na ≤ Ma∑N i = 0 with −M i − 1 ≤ N i ≤ 3

⇒ Anomaly constraint∑

Na = 0 =∑

N i satisfied

Exactly one Higgs pair∑|M i + N i | = 5

⇒ Other anomalies involving qα have to be checked independently



Constraints III – CouplingsAllowed couplings� Tree-level top: q(Hu) := −2q(10)

� Lepton Yukawas: q(eHdLi ) := qY Li

� Down-type Yukawas: q(uHdd i ) := qY di

Forbidden couplings� No µ-term: qµ = q(Hu) + q(Hd ) 6= 0� No lepton bilinears: qβi = q(Hu) + q(Li ) 6= 0

Forbidden proton decay operators� λijk 5i5j10k� ωijkl 10i10j10k5l� κijk 10i10j5k

� δijk 10i10j10k5Hd

� γi 5i5Hd 5Hu 5Hu

� κi 5Hu 5Hd 10i

All these can be expressed in terms of qµ, qY Li , qY d

i , qβi .






Forbidden couplings� No µ-term: qµ = q(Hu) + q(Hd ) 6= 0

� No lepton bilinears: qβi = q(Hu) + q(Li ) 6= 0




� κi 5Hu 5Hd 10i


i , qβi .






Forbidden couplings� No µ-term: qµ = q(Hu) + q(Hd ) 6= 0� No lepton bilinears: qβi = q(Hu) + q(Li ) 6= 0




� κi 5Hu 5Hd 10i


i , qβi .



Lessons to be learned

Satisfying the constraints� Absence of the operators λijk means that Hd must come

from a 5-curve by itself, i.e. #(fields) = MHd + NHd = 1

� The dim-5 operators ωijkl : −qµ + qY L,di induced at the

same order as µ-term and Yukawas, but from Kahlerpotential (singlets w/ opposite sign) ⇒ further suppressionpossible

� The Weinberg operator q(LiLjHuHd ) = qβi + qβj can beinduced by singlet with e.g. q(s) = 2qβi

� Absence of the operators κijk needs no triplets from theHiggs curves

� The remaining operators δijk , γi , κi remain absent as longas the βi terms are forbidden



Lessons to be learned

Satisfying the constraints� Absence of the operators λijk means that Hd must come

from a 5-curve by itself, i.e. #(fields) = MHd + NHd = 1� The dim-5 operators ωijkl : −qµ + qY L,d

i induced at thesame order as µ-term and Yukawas, but from Kahlerpotential (singlets w/ opposite sign) ⇒ further suppressionpossible

� The Weinberg operator q(LiLjHuHd ) = qβi + qβj can beinduced by singlet with e.g. q(s) = 2qβi

� Absence of the operators κijk needs no triplets from theHiggs curves

� The remaining operators δijk , γi , κi remain absent as longas the βi terms are forbidden



Scanning for models – Top-down

Observations� Models with one U(1) cannot satisfy the constraints we

impose ⇒ 4 known constructions left

� None of the known models with two U(1)’s can satisfy thelast anomaly constraints (which might be negligible):∑

i qαi qβi Ni + 3∑

a qαa qβa Na = 0 ∀α, β

ModelsSetup spectrum No anoms heavy t qλ 6=qY p stable VEVs

1 5795 140 26 18 4 22 5795 140 27 22 3 23 5795 140 34 29 0 04 5795 140 27 22 0 0





impose ⇒ 4 known constructions left� None of the known models with two U(1)’s can satisfy the

last anomaly constraints (which might be negligible):∑i qαi qβi Ni + 3

∑a qαa qβa Na = 0 ∀α, β


1 5795 140 26 18 4 22 5795 140 27 22 3 23 5795 140 34 29 0 04 5795 140 27 22 0 0








ModelsSetup spectrum

No anoms heavy t qλ 6=qY p stable VEVs

1 5795

140 26 18 4 2

2 5795

140 27 22 3 2

3 5795

140 34 29 0 0

4 5795

140 27 22 0 0








ModelsSetup spectrum No anoms

heavy t qλ 6=qY p stable VEVs

1 5795 140

26 18 4 2

2 5795 140

27 22 3 2

3 5795 140

34 29 0 0

4 5795 140

27 22 0 0








ModelsSetup spectrum No anoms heavy t

qλ 6=qY p stable VEVs

1 5795 140 26

18 4 2

2 5795 140 27

22 3 2

3 5795 140 34

29 0 0

4 5795 140 27

22 0 0








ModelsSetup spectrum No anoms heavy t qλ 6=qY

p stable VEVs

1 5795 140 26 18

4 2

2 5795 140 27 22

3 2

3 5795 140 34 29

0 0

4 5795 140 27 22

0 0








ModelsSetup spectrum No anoms heavy t qλ 6=qY p stable

VEVs

1 5795 140 26 18 4

2

2 5795 140 27 22 3

2

3 5795 140 34 29 0

0

4 5795 140 27 22 0

0









1 5795 140 26 18 4 22 5795 140 27 22 3 23 5795 140 34 29 0 04 5795 140 27 22 0 0



Scanning for models – Bottom-up

Study models in same class� Only one kind of 10-curve� Different number of 5-curves� Same charge pattern and quantization� Impose all anomaly constraints

ModelsAltogether we find O(103) models that satisfy all constraints


Conclusion


Conclusion

Model building� Find 4 MSSM-like models from F-Theory

I w/o exoticsI w/ reasonable Yukawas, suppressed proton decay and µ-term

using FN and PQ symmetries

� Anomaly freedom U(1)Y × U(1)α × U(1)β hard to satisfy� Find O(103) models in bottom-up search that satisfy all

constraints

Outlook� Calculate U(1) charges for other constructions� Check whether they can accommodate our bottom-up

models� Extend to other GUT groups



Conclusion



using FN and PQ symmetries� Anomaly freedom U(1)Y × U(1)α × U(1)β hard to satisfy

� Find O(103) models in bottom-up search that satisfy allconstraints





Conclusion



using FN and PQ symmetries� Anomaly freedom U(1)Y × U(1)α × U(1)β hard to satisfy� Find O(103) models in bottom-up search that satisfy all

constraints





Conclusion




constraints

Outlook� Calculate U(1) charges for other constructions

� Check whether they can accommodate our bottom-upmodels

� Extend to other GUT groups



Conclusion




constraints


models

� Extend to other GUT groups



Conclusion




constraints




Thank you for yourattention!

mssm-like models from string theory · fabian ruehle (desy) mssm-like models from string theory...

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