De Sitter from warped anti-D3-branes?
Ander Retolaza

Strings 2018, Okinawa, 25th June 20181707.08678 by Jakob Moritz, A.R. & Alexander Westphal

De Sitter in String Theory?
In GKP [Giddings, Kachru, Polchinski ’01] compactifications, tension between perspectives

Ander Retolaza

De Sitter from warped anti-D3-branes?

De Sitter in String Theory?
In GKP [Giddings, Kachru, Polchinski ’01] compactifications, tension between perspectives
4D EFT (SUGRA) approach to vacua
construction[Kachru, Kallosh, Linde, Trivedi ’03]

Moduli stabilization by fluxes &non-perturbative effects: AdS4
SUSYControlled uplift: localized (D3-brane on warped throat)
3.× 10-15

2.× 10-15

1.× 10-15

110120130140150

160-1.× 10-15-2.× 10-15

Ander Retolaza

De Sitter from warped anti-D3-branes?

De Sitter in String Theory?
In GKP [Giddings, Kachru, Polchinski ’01] compactifications, tension between perspectives
4D EFT (SUGRA) approach to vacua
construction[Kachru, Kallosh, Linde, Trivedi ’03]

Moduli stabilization by fluxes &non-perturbative effects: AdS4SUSY
Controlled uplift: localized (D3-brane on warped throat)
3.× 10-15

10D General Relativity[Maldacena, Núñez ’00]

Warped compactification ansatz:
Z pR4 (g 4 ) ∼g 6 e4A (Tµµ − Tmm )M6

De Sitter possible if Tµµ > Tmm
Exist in string theory, but
problematic for GKP backgrounds

2.× 10-15

D3-branes: Tµµ < Tmm

1.× 10-15

110120130140150160-1.× 10-15-2.× 10-15

Ander Retolaza

De Sitter from warped anti-D3-branes?

De Sitter in String Theory?
In GKP [Giddings, Kachru, Polchinski ’01] compactifications, tension between perspectives
4D EFT (SUGRA) approach to vacua
construction[Kachru, Kallosh, Linde, Trivedi ’03]

Moduli stabilization by fluxes &non-perturbative effects: AdS4
SUSYControlled uplift: localized (D3-brane on warped throat)
3.× 10-15

10D General Relativity[Maldacena, Núñez ’00]

Warped compactification ansatz:
Z p
R4 (g 4 ) ∼g 6 e4A (Tµµ − Tmm )M6

De Sitter possible if Tµµ > Tmm
Exist in string theory, but
problematic for GKP backgrounds

2.× 10-15

D3-branes: Tµµ < Tmm

1.× 10-15

110120130140150160-1.× 10-15-2.× 10-15[Mortiz, AR, Westphal ’17]

10D picture of most simple KKLT construction

Ander Retolaza

De Sitter from warped anti-D3-branes?

10D picture of KKLT
Start with 2 derivative Type IIB action. For a generalized GKP ansatz:
 IASD 2
Zp |G3 |∆loc
R4 (g 4 ) ∼ d 6 y g 6 −|∂(e4A − α)|2 − e8A+6Im(τ )2πAnder Retolaza

De Sitter from warped anti-D3-branes?

10D picture of KKLT
Start with 2 derivative Type IIB action. For a generalized GKP ansatz:
 IASD 2Zp |G3 |∆loc
R4 (g 4 ) ∼ d 6 y g 6 −|∂(e4A − α)|2 − e8A+6Im(τ )2π
We can now follow the KKLT approach:
Moduli stabilization: fluxes and one gaugino condensate hλλi (h1,1 = 1)
10D description of hλλi using [Baumann, Dymarsky, Kachru, Klebanov, McAllister ’10]Z
R4 (g 4 ) ∼ −|hλλi|2|F (z)|2 ≤ 0
X
M6 0Ander Retolaza

De Sitter from warped anti-D3-branes?

10D picture of KKLT
Start with 2 derivative Type IIB action. For a generalized GKP ansatz:
 IASD 2Zp |G3 |∆loc
R4 (g 4 ) ∼ d 6 y g 6 −|∂(e4A − α)|2 − e8A+6Im(τ )2π
We can now follow the KKLT approach:
Moduli stabilization: fluxes and one gaugino condensate hλλi (h1,1 = 1)
10D description of hλλi using [Baumann, Dymarsky, Kachru, Klebanov, McAllister ’10]Z
R4 (g 4 ) ∼ −|hλλi|2|F (z)|2 ≤ 0X
M6 0A D3-brane in a highly warped throat must contributebut −e8A ∆loc ∼ e8A0 T3  e4A0 T3 .

Ander Retolaza∼ e4A0 T3

De Sitter from warped anti-D3-branes?

10D picture of KKLT
Start with 2 derivative Type IIB action. For a generalized GKP ansatz:
 IASD 2Zp |G3 |∆loc
R4 (g 4 ) ∼ d 6 y g 6 −|∂(e4A − α)|2 − e8A+6Im(τ )2π
We can now follow the KKLT approach:
Moduli stabilization: fluxes and one gaugino condensate hλλi (h1,1 = 1)
10D description of hλλi using [Baumann, Dymarsky, Kachru, Klebanov, McAllister ’10]
Z|F (z)|2 ≤ 0X
R4 (g 4 ) ∼ −|hλλi|2M6 0A D3-brane in a highly warped throat must contributebut −e8A ∆loc ∼ e8A0 T3  e4A0 T3 .

∼ e4A0 T3

Leading order correction to R4 from re-adjustment of internal geometry:in the controlled regime a warped D3-brane fails to uplift to de Sitter

Ander Retolaza

De Sitter from warped anti-D3-branes?