on scale separation a membrane/potential correspondence

On Scale Separation &

a Membrane/Potential Correspondence

October 20, 2020

Seminar Series on String Phenomenology

Alvaro HerraezIPhT CEA/Saclay

Based on: A. Font, AH, Luis E. Ibáñez [arXiv:1912.03317]

AH [arXiv: 2006.01160]

https://arxiv.org/abs/1912.03317

https://arxiv.org/abs/2006.01160

On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020

Outline

1. Scale separation in a class of Type II orientifolds

(i) The Swampland, Scale separation and the ADC

(ii) A Type IIA toroidal example

(iii)A Type IIB toroidal example

2. Membranes and the Flux Potential

(i) 4-forms and the Flux potential

(ii) Interactions between membranes

3. Conclusions


Scale Separation in a class of

Type IIA orientifolds


• String Landscape

• Swampland

The Landscape vs the Swampland

Naive expectation: Every EFT can be obtained from ST

Set of EFT that look consistent BUT cannot be consistently coupled to QG[Vafa ’05]

Reviews: [Brennan, Carta, Vafa ’17] [Palti ’19]



• Swampland




QUESTION: What are the general

features of all QG EFT?




• Swampland




QUESTION: What are the general

features of all QG EFT?

Quantum Gravity Conjectures



The Swampland Conjectures


Scale Separation and the ADC

Anti de-Sitter Distance Conjecture: In a theory of quantum gravity with cosmological constant there exist a tower of states that becomes light in the limit

, whose masses behave as

ΛΛ → 0

(SUSY case)γ = 12m ∼ Mp

ΛM2p

γ

[Gautason, Schillo, Van Riet, Williams ’16][Duff, Nilsson, Pope ’86] [Douglas, Kachru ’07] [Tsimpis ’12]

[Lüst, Palti, Vafa ’19]





ΛΛ → 0


ΛM2p

γ


If this tower is the KK-tower and γ = 12

Rint ∼ Rext






ΛΛ → 0


ΛM2p

γ



Rint ∼ Rext

NO Scale Separation






ΛΛ → 0


ΛM2p

γ



Rint ∼ Rext

Crucial for uplifting mechanisms NO Scale Separation



Moduli RR-fluxes NSNS-fluxes

• Playground: Isotropic type IIA toroidal orientifold with fluxes

Scale Separation on a Type IIA orientifold

S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h( M, c, e, e0 )





S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h

∑α

([Πα] + [ℛΠα]) −m [ΠH] −4 [ΠO6] = 0

( M, c, e, e0 )

• Superpotential: W = e0 + 3ieT + 3cT2 + iMT3 + ih 0S−3ih U

• Tadpole Cancelation condition:





S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h

∑α

([Πα] + [ℛΠα]) −m [ΠH] −4 [ΠO6] = 0

• There are vacua with scale separation OK in the 4d picture BUT 10d uplift?

[DeWolfe, Giryavets, Kachru, Taylor '05][Cámara, Font, Ibáñez ’05]

[Blumenhagen, Brinkmann, Makridou ’19] [Junghans ’20] [Buratti, Calderon, Mininno, Uranga '20] [Marchesano, Palti, Quirant, Tomasiello ’20]

( M, c, e, e0 )

• Superpotential: W = e0 + 3ieT + 3cT2 + iMT3 + ih 0S−3ih U





S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )

• Superpotential: W = e0 + 3ieT + 3cT2 + iMT3 + ih 0S−3ih U −3aST −3bTU

Moduli RR-fluxes NSNS-fluxes Metric fluxes

a, fdηm = ωm

np ηn∧ ηp

h 0 M + 3ac = 0M h + fc = 0




S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp

h 0 M + 3ac = 0M h + fc = 0• SUSY AdS vacua with

Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4

[Cámara, Font, Ibáñez ’05]




S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp


Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4


0a, f → ∞




S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp


Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4

10d uplift: AdS3 × S3 × S3

[Aldazábal, Font ’07]

• Correction to the internal volume

Vol�S3 ⇥ S3

�= C t3

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C ' 1

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[Lüst, Tsimpis ’05]

[Graña, Minasian, Petrini, Tomasiello ’05 ’07]


ds2 = e2A(y) ̂g μνd xμd xν + g mndymdyn• Warped Metric




S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp


Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4




Vol�S3 ⇥ S3

�= C t3


C ' 1




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1

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S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp


Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4




Vol�S3 ⇥ S3

�= C t3


C ' 1






1


Flux Independent!

1[Cámara, Font, Ibáñez ’05]





S, U, T F0, F2, F4, F6 H3

Complex Structure

Kählerh 0, h


( M, c, e, e0 )



a, fdηm = ωm

np ηn∧ ηp


Λ ≃ (af3) M3

c5

M2KK ≃ (af3)1/2 M3

c5

MKK

|Λ |1/2 ≃ 1

(af 3)1/4






Vol�S3 ⇥ S3

�= C t3


C ' 1






1


Flux Independent!

1ADC fulfilledADC fulfilled


• Playground: Isotropic type IIB toroidal orientifold with non-geometric fluxes

Scale Separation on a Type IIB orientifold

S ⟷ S U ⟷ T

• Superpotential: W = e0 + 3ieU + 3cU2 + iMU3 + ih 0S−3ih T −3aSU −3bTU

T-dual of type IIA with geometric fluxes:




S ⟷ S U ⟷ T



• SUSY AdS vacua with

Λ ≃ (af3) c1/2

e3/20

M2KK ≃ f

(ce0)1/2

MKK

|Λ |1/2 ≃ e1/40

c1/4 (af )1/2

[Blumenhagen, Font,

Fuchs, Herschmann,

Plauschinn,

Sekiguchi, Wolf ’15]




S ⟷ S U ⟷ T




Λ ≃ (af3) c1/2

e3/20

M2KK ≃ f

(ce0)1/2

MKK

|Λ |1/2 ≃ e1/40

c1/4 (af )1/2 ∞e0 → ∞

[Blumenhagen, Font,

Fuchs, Herschmann,

Plauschinn,

Sekiguchi, Wolf ’15]Scale Separation!




S ⟷ S U ⟷ T




Λ ≃ (af3) c1/2

e3/20

M2KK ≃ f

(ce0)1/2

MKK

|Λ |1/2 ≃ e1/40

c1/4 (af )1/2 ∞e0 → ∞

[Blumenhagen, Font,

Fuchs, Herschmann,

Plauschinn,


• BUT… Recall that to go from IIA to IIB one performs three T-dualities along the three “x-directions” of the torus The scale asociated to is untouched Calculate it in the fully backreacted 10d solution in IIA

MyKK

Scale Separation!




S ⟷ S U ⟷ T




Λ ≃ (af3) c1/2

e3/20

M2KK ≃ f

(ce0)1/2

MKK

|Λ |1/2 ≃ e1/40

c1/4 (af )1/2 ∞e0 → ∞

NO Scale Separation!

[Blumenhagen, Font,

Fuchs, Herschmann,

Plauschinn,



MyKK

MKK

|Λ |1/2 ≃ 1




S ⟷ S U ⟷ T




Λ ≃ (af3) c1/2

e3/20

M2KK ≃ f

(ce0)1/2

MKK

|Λ |1/2 ≃ e1/40

c1/4 (af )1/2 ∞e0 → ∞

NO Scale Separation!

[Blumenhagen, Font,

Fuchs, Herschmann,

Plauschinn,



MyKK

MKK

|Λ |1/2 ≃ 1 ADC


Membranes &

the Flux Potential


• Consider the action for a 3-form in 4d

• Equation of motion (away from the membranes)

S = �Z

d4x1

2|F4|2 + q

Z

D3

C3 + Sbound

Fµ⌫⇢� = f0✏µ⌫⇢�

Kinetic terms

Coupling to membranes

[Brown, Teitelboim, Bousso, Polchinski, Dvali…]

3-forms and Membranes


• Consider the action for a 3-form in 4d


S = �Z

d4x1

2|F4|2 + q

Z

D3

C3 + Sbound

Fµ⌫⇢� = f0✏µ⌫⇢�

Kinetic terms



No propagating dof in 4d

3-forms and Membranes


3-forms and Membranes• Consider the action for a 3-form in 4d


• Membranes separate different vacua labelled by the value of

S = �Z

d4x1

2|F4|2 + q

Z

D3

C3 + Sbound

Fµ⌫⇢� = f0✏µ⌫⇢�

f0

At this level is undetermined q

Kinetic terms


No propagating dof in 4d



• The scalar potential in N=1 flux compactifications can be expressed as:

Membranes and the Flux Potential

V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )[Cremmer et al.]

[Bandos, Bielleman, Carta, Dudas, Farakos, AH, Ibáñez, Lanza, Marchesano, Martucci, Staessens, Valenzuela, Zoccarato ’15-20]

V = ZAB

2 qAqBS = �1

8

ZZABF

A4 ^ ⇤4FB

4 +1

4

ZFA4 qA

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• The scalar potential in N=1 flux compactifications can be expressed as:

• Consider two parallel BPS membranes


• QUESTION: Can we interpret the different contributions to the scalar potential in terms of interactions between the membranes which source the corresponding fluxes?

V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )

T = 2eK/2 |W |

[Cremmer et al.]

[Bandos, Bielleman, Carta, Dudas, Farakos, AH, Ibáñez, Lanza, Marchesano, Martucci, Staessens, Valenzuela, Zoccarato ’15-20]

V = ZAB

2 qAqBS = �1

8

ZZABF

A4 ^ ⇤4FB

4 +1

4

ZFA4 qA

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V = ZAB

2 qAqB


• Calculate the following interactions

h μν



V = ZAB

2 qAqB



Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄) SΦ,kin = 1

κ24 ∫ −g d 4x KIJ̄∂μΦI∂μΦ̄J̄

h μν



V = ZAB

2 qAqB



SCS = Q∫WVC3

h μν



S3,kin = 12κ2 ∫ ZABFA ∧ *FB



V = ZAB

2 qAqB



SCS = Q∫WVC3

h μν

Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄)



S3,kin = 12κ2 ∫ ZABFA ∧ *FB

SEH = 12κ2 ∫ d Dx −g R



V = ZAB

2 qAqB



h μν

−eKKIJ̄ DIWDJ̄W̄

∼ 12 ZABQAQB

∼ 3eK |W |2


Membranes and the Flux Potential• Calculate the following interactions

h μν

−eKKIJ̄ DIWDJ̄W̄

∼ 12 ZABQAQB

∼ 3eK |W |2

Scalar Potential = Membrane interaction

Relations between Conjectures[See Lanza, Marchesano, Martucci, Valenzuela ’20]


Conclusions

2. Equivalence between N=1 flux induced scalar potential and BPS membrane interactions

Potential relations between Conjectures

1. Corrections from internal backreaction (in this class of models)

Scale Separation disappears/ADC is fulfilled

on scale separation a membrane/potential correspondence

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