ADS-PHOBIA:

CONFRONTING THE SM AND SUSY WITH THE WGC

Alvaro Herráez Universidad Autónoma de Madrid & Instituto de Física Teórica UAM-CSIC

Based on: E. Gonzalo, A. H., L. E. Ibáñez [1803.08455]

String Pheno 2018, Warsaw July 4, 2018

•

THE SWAMPLAND AND ADS-PHOBIA

SWAMPLAND

LANDSCAPE

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

THE SWAMPLAND AND ADS-PHOBIA

[See Irene’s talk]

• Refined WGC WGC inequality is strict for non-SUSY states

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

[Ooguri, Vafa ’17]Corolarium

THE SWAMPLAND AND ADS-PHOBIA

Stable non-SUSY AdS vacua belong to the SWAMPLAND

[See Irene’s talk]

• Refined WGC WGC inequality is strict for non-SUSY states

• Background independence A theory must be consistent in any BG

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

[Ooguri, Vafa ’17]Corolarium

THE SWAMPLAND AND ADS-PHOBIA

Stable non-SUSY AdS vacua belong to the SWAMPLAND

[See Irene’s talk]

• Refined WGC WGC inequality is strict for non-SUSY states

• Background independence A theory must be consistent in any BG

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

[Ooguri, Vafa ’17]Corolarium

SM

THE SWAMPLAND AND ADS-PHOBIA

Stable non-SUSY AdS vacua belong to the SWAMPLAND

[See Irene’s talk]

• Refined WGC WGC inequality is strict for non-SUSY states

• Background independence A theory must be consistent in any BG

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

[Ooguri, Vafa ’17]Corolarium

Stable non-SUSY AdS vacua belong to the SWAMPLAND

SM

THE SWAMPLAND AND ADS-PHOBIA

[See Irene’s talk]

• Refined WGC WGC inequality is strict for non-SUSY states

• Background independence A theory must be consistent in any BG

General Features of all QG EFT

QG Conjectures

SWAMPLAND

LANDSCAPE

[Ooguri, Vafa ’17]Corolarium

SM

THE SWAMPLAND AND ADS-PHOBIA

Stable non-SUSY AdS vacua belong to the SWAMPLAND

[See Irene’s talk]

• Compactify the SM+GR to 3d or 2d SM landscape[Arkani-Hamed, Dubovski, Nicolis, Villadoro ’07]

ADS-PHOBIA AND THE SM

[Arnold, Fornal, Wise ’10]

• Compactify the SM+GR to 3d or 2d SM landscape

• SM+GR on the circle Radius is a massless field

[Arkani-Hamed, Dubovski, Nicolis, Villadoro ’07]

ADS-PHOBIA AND THE SM

[Arnold, Fornal, Wise ’10]

R

V (R) ' 2⇡⇤4

R2

• Compactify the SM+GR to 3d or 2d SM landscape

• SM+GR on the circle Radius is a massless field

[Arkani-Hamed, Dubovski, Nicolis, Villadoro ’07]

ADS-PHOBIA AND THE SM

[Arnold, Fornal, Wise ’10]

R

V (R) ' 2⇡⇤4

R2+X

p

V Cp

• Compactify the SM+GR to 3d or 2d SM landscape

• SM+GR on the circle Radius is a massless field

[Arkani-Hamed, Dubovski, Nicolis, Villadoro ’07]

ADS-PHOBIA AND THE SM

[Arnold, Fornal, Wise ’10]

R

V (R) ' 2⇡⇤4

R2+X

p

V Cp

• Massless particles V (R) ⇠ ± np

R6

• Massive particles V (R) ⇠ e�mpR if mp � R�1

V (R) ⇠ ± np

R6if mp ⌧ R�1

Casimir Energy

• Compactify the SM+GR to 3d or 2d SM landscape

• SM+GR on the circle Radius is a massless field

[Arkani-Hamed, Dubovski, Nicolis, Villadoro ’07]

ADS-PHOBIA AND THE SM

[Arnold, Fornal, Wise ’10]

R

V (R) ' 2⇡⇤4

R2+X

p

V Cp

• Massless particles V (R) ⇠ ± np

R6

• Massive particles V (R) ⇠ e�mpR if mp � R�1

V (R) ⇠ ± np

R6if mp ⌧ R�1

- Bosons + (periodic) Fermions

Casimir Energy

ADS-PHOBIA AND THE SM• Photon, graviton and neutrinos first particles to enter the game �, g, ⌫

�2� 2+6

+12

(M)

(D)

ADS-PHOBIA AND THE SM

-���� -���� -���� -��� -��� -��� -���-�

-�

�

�

�

�

�

�

Majorana neutrinos Dirac neutrinos

�, g, ⌫

�2� 2+6

+12

(M)

(D)

Small RSmall R

[Ibáñez, Martin-Lozano, Valenzuela ’17]

• Photon, graviton and neutrinos first particles to enter the game

ADS-PHOBIA AND THE SM

-���� -���� -���� -��� -��� -��� -���-�

-�

�

�

�

�

�

�

Majorana neutrinos Dirac neutrinos

AdS vacuum always forms!

�, g, ⌫

�2� 2+6

+12

(M)

(D)

Small RSmall R

[Ibáñez, Martin-Lozano, Valenzuela ’17]

• Photon, graviton and neutrinos first particles to enter the game

ADS-PHOBIA AND THE SM

-���� -���� -���� -��� -��� -��� -���-�

-�

�

�

�

�

�

�

Majorana neutrinos Dirac neutrinos

SWAMPLAND!

�, g, ⌫

�2� 2+6

+12

(M)

(D)

Small RSmall R

[Ibáñez, Martin-Lozano, Valenzuela ’17]

• Photon, graviton and neutrinos first particles to enter the game

ADS-PHOBIA AND THE SM

-���� -���� -���� -��� -��� -��� -���-�

-�

�

�

�

�

�

�

Majorana neutrinos Dirac neutrinos

SWAMPLAND! Can avoid AdS if masses are light enough

�, g, ⌫

�2� 2+6

+12

(M)

(D)

Small RSmall R

[Ibáñez, Martin-Lozano, Valenzuela ’17]

• Photon, graviton and neutrinos first particles to enter the game

ADS-PHOBIA AND THE SM

• But…

More particles as R decreases

Higgs potential

Wilson Lines (WL)

1

2

3

ADS-PHOBIA AND THE SM

• But…

More particles as R decreases

Higgs potential

Wilson Lines (WL)

-�� -� � �

�

��

��

��

Small R

1

[Hamada, Shiu ’17][Gonzalo, A.H., Ibáñez ’18]

1

2

3

ADS-PHOBIA AND THE SM

• But…

More particles as R decreases

Higgs potential

Wilson Lines (WL)

2

[Gonzalo, A.H., Ibáñez ’18]1

2

3

ADS-PHOBIA AND THE SM

• But…

More particles as R decreases

Higgs potential

Wilson Lines (WL)

3 � Wilson Line

[Hamada, Shiu ’17][Gonzalo, A.H., Ibáñez ’18]1

2

3

ADS-PHOBIA AND THE SM

• But…

More particles as R decreases

Higgs potential

Wilson Lines (WL)

3

Runaway directions Destabilize the minima

� Wilson Line

[Hamada, Shiu ’17][Gonzalo, A.H., Ibáñez ’18]1

2

3

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to an orbifold

24

S1/Z2

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to an orbifold

24

S1/Z2 It’s NOT a symmetry

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to a TORUS orbifold

24

T 2/Z4

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to a TORUS orbifold

24

T 2/Z4

y1 �! �y2

y2 �! y1

�(xi, y1, y2) = eiq↵�(xi,�y2, y1)

Project under π/2 rotations

(xi, y1, y2) = eiq↵ei⇡4 �3 (xi,�y2, y1)

Fix the complex structure Only surviving scalar: area

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to a TORUS orbifold

24

T 2/Z4

y1 �! �y2

y2 �! y1

�(xi, y1, y2) = eiq↵�(xi,�y2, y1)

(xi, y1, y2) = eiq↵ei⇡4 �3 (xi,�y2, y1)

Internal action(gauge group)

Fix the complex structure Only surviving scalar: area

Project under π/2 rotations

THE SM ON T / Z

• Want to find a way to fix the WL in order to have predictability

Go to a TORUS orbifold

• gauge embeddings

• Cartan subalgebra of the SM:

• Gaugeable

• R-symmetries (in SUSY extensions)

24

T 2/Z4

y1 �! �y2

y2 �! y1

�(xi, y1, y2) = eiq↵�(xi,�y2, y1)

(xi, y1, y2) = eiq↵ei⇡4 �3 (xi,�y2, y1)

Internal action(gauge group)

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

U(1)B�L

Fix the complex structure Only surviving scalar: area

Project under π/2 rotations

THE SM ON T / Z

• gauge embeddings

• Cartan subalgebra of the SM:

24

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

-�� -� � �

-�

�

�

��

��

��

Small R

THE SM ON T / Z

• gauge embeddings

• Cartan subalgebra of the SM:

24

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

-�� -� � �

-�

�

�

��

��

��

Small R

The SM by itself is in the SWAMPLAND

It is “TOO FERMIONIC”

THE SM ON T / Z

• gauge embeddings

• Cartan subalgebra of the SM:

24

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

-�� -� � �

-�

�

�

��

��

��

Small R

The SM by itself is in the SWAMPLAND

It is “TOO FERMIONIC”

SUSY extension

THE SM ON T / Z

• gauge embeddings

• Cartan subalgebra of the SM:

24

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

Small R

Creates a runaway

SUSY extension

-�� -� � �-��

-��

-��

-��

�

��

��

• gauge embeddings

• Cartan subalgebra of the SM:

24

Z4

SU(3)c ⇥ SU(2)L ⇥ U(1)Y

Small R

Creates a runaway

-�� -� � �-��

-��

-��

-��

�

��

��

THE MSSM ON T / Z

• gauge embeddings

• Gaugeable

24

Z4

Small R

THE MSSM ON T / Z

U(1)B�L

-�� -� � �

�

��

��

�� Superpartners do not

contribute to the Casimir energy

• gauge embeddings

• Gaugeable

24

Z4

Small R

THE MSSM ON T / Z

U(1)B�L

-�� -� � �

�

��

��

��

Recover neutrino bounds

Superpartners do not contribute to the Casimir energy

• gauge embeddings

• R-symmetry

24

Z4

Small R

THE MSSM ON T / Z

-�� -� � �

�

��

��

��

The whole spectrum contributes to the Casimir energy When all particles enter the game, the leading part cancels

• gauge embeddings

• R-symmetry

24

Z4

Small R

THE MSSM ON T / Z

-�� -� � �

�

��

��

��

The whole spectrum contributes to the Casimir energy When all particles enter the game, the leading part cancels

The next order decides wether the potential goes to :

�SS 0 =) V ! �1

�SS � 0 =) V ! +1

• gauge embeddings

• R-symmetry

24

Z4

Small R

THE MSSM ON T / Z

-�� -� � �

�

��

��

��

The whole spectrum contributes to the Casimir energy When all particles enter the game, the leading part cancels

The next order decides wether the potential goes to :

�SS 0 =) V ! �1

�SS � 0 =) V ! +1

Constrain mass spectrum

• gauge embeddings

• R-symmetry

24

Z4

Small R

THE MSSM ON T / Z

The whole spectrum contributes to the Casimir energy When all particles enter the game, the leading part cancels

The next order decides wether the potential goes to :

�SS 0 =) V ! �1

�SS � 0 =) V ! +1

-�� -� � �

�

��

��

��

Constrain mass spectrum

CONCLUSIONS

• SM as it is has stable AdS vacua in 2d SWAMPLAND

• SUSY extensions destabilise them Consistent with QG

• If SUSY extension contains a gaugeable

• Majorana neutrinos Swampland

• Dirac neutrinos Mass upper bound

• Bounds for the EW scale

• If SUSY extension contains an R-symmetry Constrains on the spectrum (supertrace)

U(1)B�L

m⌫3 1⇥ 10�3

eV (IH)

m⌫1 4⇥ 10�3

eV (NH)

[See E. Gonzalo’s talk]⇤QCD hHi 1 TeV

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CONCLUSIONS

• SM as it is has stable AdS vacua in 2d SWAMPLAND

• SUSY extensions destabilise them Consistent with QG

• If SUSY extension contains a gaugeable

• Majorana neutrinos Swampland

• Dirac neutrinos Mass upper bound

• Bounds for the EW scale

• If SUSY extension contains an R-symmetry Constrains on the spectrum (supertrace)

U(1)B�L

m⌫3 1⇥ 10�3

eV (IH)

m⌫1 4⇥ 10�3

eV (NH)

[See E. Gonzalo’s talk]⇤QCD hHi 1 TeV

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