On Scale Separation a Membrane/Potential Correspondence
Transcript of 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]
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
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Scale Separation in a class of
Type IIA orientifolds
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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]
QUESTION: What are the general
features of all QG EFT?
Reviews: [Brennan, Carta, Vafa ’17] [Palti ’19]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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]
QUESTION: What are the general
features of all QG EFT?
Quantum Gravity Conjectures
Reviews: [Brennan, Carta, Vafa ’17] [Palti ’19]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
The Swampland Conjectures
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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
[Lüst, Palti, Vafa ’19]
If this tower is the KK-tower and γ = 12
Rint ∼ Rext
[Gautason, Schillo, Van Riet, Williams ’16][Duff, Nilsson, Pope ’86] [Douglas, Kachru ’07] [Tsimpis ’12]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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
[Lüst, Palti, Vafa ’19]
If this tower is the KK-tower and γ = 12
Rint ∼ Rext
NO Scale Separation
[Gautason, Schillo, Van Riet, Williams ’16][Duff, Nilsson, Pope ’86] [Douglas, Kachru ’07] [Tsimpis ’12]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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
[Lüst, Palti, Vafa ’19]
If this tower is the KK-tower and γ = 12
Rint ∼ Rext
Crucial for uplifting mechanisms NO Scale Separation
[Gautason, Schillo, Van Riet, Williams ’16][Duff, Nilsson, Pope ’86] [Douglas, Kachru ’07] [Tsimpis ’12]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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 )
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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
∑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:
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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
∑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
• Tadpole Cancelation condition:
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• 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]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• 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]
0a, f → ∞
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• SUSY AdS vacua with
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]
[Cámara, Font, Ibáñez ’05]
ds2 = e2A(y) ̂g μνd xμd xν + g mndymdyn• Warped Metric
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• SUSY AdS vacua with
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]
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[Cámara, Font, Ibáñez ’05]
ds2 = e2A(y) ̂g μνd xμd xν + g mndymdyn• Warped Metric
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• SUSY AdS vacua with
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]
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1
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Flux Independent!
1[Cámara, Font, Ibáñez ’05]
ds2 = e2A(y) ̂g μνd xμd xν + g mndymdyn• Warped Metric
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
• Tadpole Cancelation condition:
( 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• 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]
10d uplift: AdS3 × S3 × S3
[Aldazábal, Font ’07]
ds2 = e2A(y) ̂g μνd xμd xν + g mndymdyn• Warped Metric
• 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]
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1
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Flux Independent!
1ADC fulfilledADC fulfilled
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
• 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]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
• 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 ∞e0 → ∞
[Blumenhagen, Font,
Fuchs, Herschmann,
Plauschinn,
Sekiguchi, Wolf ’15]Scale Separation!
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
• 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 ∞e0 → ∞
[Blumenhagen, Font,
Fuchs, Herschmann,
Plauschinn,
Sekiguchi, Wolf ’15]
• 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!
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
• 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 ∞e0 → ∞
NO Scale Separation!
[Blumenhagen, Font,
Fuchs, Herschmann,
Plauschinn,
Sekiguchi, Wolf ’15]
• 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
MKK
|Λ |1/2 ≃ 1
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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:
• 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 ∞e0 → ∞
NO Scale Separation!
[Blumenhagen, Font,
Fuchs, Herschmann,
Plauschinn,
Sekiguchi, Wolf ’15]
• 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
MKK
|Λ |1/2 ≃ 1 ADC
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes &
the Flux Potential
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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…]
No propagating dof in 4d
3-forms and Membranes
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
3-forms and Membranes• Consider the action for a 3-form in 4d
• Equation of motion (away from the membranes)
• 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
Coupling to membranes
No propagating dof in 4d
[Brown, Teitelboim, Bousso, Polchinski, Dvali…]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• 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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On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
• The scalar potential in N=1 flux compactifications can be expressed as:
• Consider two parallel BPS membranes
Membranes and the Flux Potential
• 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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On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes and the Flux Potential
V = ZAB
2 qAqB
V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )
• Calculate the following interactions
h μν
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes and the Flux Potential
V = ZAB
2 qAqB
V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )
• Calculate the following interactions
Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄) SΦ,kin = 1
κ24 ∫ −g d 4x KIJ̄∂μΦI∂μΦ̄J̄
h μν
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes and the Flux Potential
V = ZAB
2 qAqB
V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )
• Calculate the following interactions
SCS = Q∫WVC3
h μν
Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄) SΦ,kin = 1
κ24 ∫ −g d 4x KIJ̄∂μΦI∂μΦ̄J̄
S3,kin = 12κ2 ∫ ZABFA ∧ *FB
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes and the Flux Potential
V = ZAB
2 qAqB
V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )
• Calculate the following interactions
SCS = Q∫WVC3
h μν
Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄)
Smem = −∫WVd 3ξ g ab T (ΦI, Φ̄J̄) SΦ,kin = 1
κ24 ∫ −g d 4x KIJ̄∂μΦI∂μΦ̄J̄
S3,kin = 12κ2 ∫ ZABFA ∧ *FB
SEH = 12κ2 ∫ d Dx −g R
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
Membranes and the Flux Potential
V = ZAB
2 qAqB
V = eK (KIJ̄ DIWDJ̄W̄ −3 |W |2 )
• Calculate the following interactions
h μν
−eKKIJ̄ DIWDJ̄W̄
∼ 12 ZABQAQB
∼ 3eK |W |2
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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]
On Scale Separation and a Membrane/Potential Correspondence Seminar Series on String Phenomenology 2020
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