Luca Martucci Recent swampland conjectures imply no de Sitter vacua - - PowerPoint PPT Presentation

Galileo Galilei DIPARTIMENTO DI FISICA E ASTRONOMIA D A F

a

Luca Martucci

Recent swampland conjectures imply no de Sitter vacua in string theory! Popular KKLT-like de Sitter models:

crucially involves anti-branes combines 10d and 4d EFT arguments

Is there anything WRONG?

In this talk:

4d EFTs for anti-brane goldstino KKLT from 10d

[Ooguri, Palti, Shiu, Vafa `18] [Obied, Ooguri, Spodyneiko, Vafa `18] [Dvali, Gomez `18] [Bandos-LM-Sorokin-Tonin`16] [Bandos-Heller-Kuzenko-LM-Sorokin`16] [Koerber, L.M. `08] [Dymarsky, L.M. `10] [Baumann, Dymarsky, Kachru, Klebanov, McAllister `10] [Hamada, Hebecker, Shiu, Soler `18-`19] [Moriz, Retolaza Westaphal `17] [Carta, Moritz, Westphal `19] [Gautason, Van Hemelryck, Van Riet, Venken `19] [Bena, Graña, Kovensky, Retolaza `19] [Kachru, Kim, McAllister, Zimet `19] [Kallosh `18]

Anti-branes, goldstino and EFTs

KKLT anti-brane ideology

hλλi 6= 0

ds2

10 = e2Ads2 4 + e−2Ads6

[Kachru-Kallosh- Linde,Trivedi `03]

KKLT anti-brane ideology

hλλi 6= 0

ds2

10 = e2Ads2 4 + e−2Ads6

[Kachru-Kallosh- Linde,Trivedi `03]

K = −3 log(Imρ)

+

VD3 = µ4 (Imρ)2

KKL(MM)T `03

4d EFT? by probe approach:

W = W0 + A e

2πiρ N

N=1 SUSY EFT

Non-linear realizations through nilpotent superfield

W = W0 + A e2πiρ+µ2MP S

S2 = 0

[Ferrara-Kallosh- Linde `14]

VD3 = µ4 (Imρ)2

K = −3 log(Imρ−S ¯ S)

(neglecting scalar and U(1) gauge field on )

D3

[KKLT+ Maldacena & McAllister `03]

Does it support probe result? Not really!

basically any potential (and non-susy interaction) can be supersymmetrized! “Elementary” constrained superfields:

natural EFT in 4d spontaneous SUSY-breaking

Not the case in anti-brane models: alternative formulation?

Goldstino brane

[Bandos-LM-Sorokin-Tonin`16] [Bandos-Heller-Kuzenko-LM-Sorokin`16]

Goldstino Brane

B4

M4|4

induced vielbein: ea(ξ) = ∂izMEM

a(z(ξ))dξi

Simplest brane action:

[f] = (mass)2

SG = −f 2 Z

B4

d4ξ det e(ξ)

SDiff(M4|4)

+ local Lorentz

(local) N = 1

zM(ξ) = (xm(ξ), θα(ξ), ¯ θ ˙

α(ξ))

world-volume fields:

Diff(B4)

θα(ξ)

Goldstino

xm(ξ) pure gauge

Goldstino Brane

B4

M4|4

Simplest example: flat superspace static gauge:

xm(ξ) = δm

i ξi

Ea = δa

mdxm + iθσad¯

θ − idθσa¯ θ

χα(x) ≡ fθα(x)

canonical goldstino:

ea = δa

mdxm + i f −2 (χσad¯

χ − dχσa ¯ χ)

Volkov-Akulov goldstino action!

SG = −f 2 Z

B4

d4ξ det e(ξ) = −f 2 + i¯ χ/ ∂χ + . . . ≡ LVA

Goldstino Brane

B4

M4|4

Coupling to supergravity immediate:

S = −3M 2

P

Z d4xd4θ E + 2 ✓ W0 Z d4xd2θ E + c.c. ◆ − f 2 Z d4ξ det e(ξ)

• Z ✓

¯ χ / rχ + f ¯ χγmψm + W0 M 2

P

¯ χχ + . . . ◆

= M 2

P

Z d4xpg ✓1 2 R ¯ ψmγmnprnψp + W0 ¯ ψR

mγmnψR n + . . .

◆

• Z

d4xpg ✓ f 2 3|W0|2 M 2

P

◆

Goldstino Brane

B4

M4|4

Coupling to NON-supersymmetric matter, e.g. world-volume scalar :

ϕ(ξ)

S = − Z d4ξ det e(ξ)

• gij∂iϕ∂jϕ + V (ϕ)
• <latexit sha1_base64="yGDMGQJ4SGgNw1K54DTbLfYUGP4=">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</latexit>

can be applied to scalars and vector on in KKLT D3

= − Z d4x√−g [gmn∂mϕ∂nϕ + V (ϕ)] + (goldstino+gravity multiplet)

Goldstino Brane

B4

M4|4

Coupling to supersymmetric matter:

any potential can be directly supersymmetrized!

= Z d4x√−g V (φ) + (goldstino + gravity & matter multiplets)

Φ(z) = φ(x) + θψ(x) + . . .

Φ(z(ξ)) = φ(x(ξ)) + f −1χ(ξ)ψ(x(ξ)) + . . .

SG = − Z V (Φ(z(ξ))) det e(ξ)

E.g.

VD3 = µ4 (Imρ)2

in KKLT

Nice… but a lot of freedom! Main point, so far: Goldstino brane as natural EFT for anti-branes Matching with UV-theory?

geometrizes (compensator) Stückelberg trick

[Delacretaz-Gorbenko-Senatore `16]

manifest “brany” nature (GS-formulation) natural coupling of brane non-susy and bulk susy matter application to Carlo’ s constructions? immediate generalization to models

d 6= 4

Back to string compactifications

The KKLT scenario

Tree-level solution

[Giddings-Kachru-Polchinski `01]

4d EFT:

no-scale Minkowski vacuum

ds2

10 = e2Ads2 4 + e−2Ads6

W = W0 = Z Ω ∧ G3

K = −3 log(Imρ)

The KKLT scenario

K = −3 log(Imρ)

4d EFT:

AdS vacuum

hλλi 6= 0

ds2

10 = e2Ads2 4 + e−2Ads6

Tree-level solution + gaugino condensate under control if:

hImρi ⇠ 2π N log

• A

W0

• 1

|W0| ⇠ e− 2πhIm ρi

N

⌧ 1

|hV i| ⇠ e− 4πhIm ρi

N

⌧ 1

W = W0+A e

2πiρ N

The KKLT scenario

Tree-level solution + gaugino condensate+ anti-D3-brane

dS vacuum

hλλi 6= 0

ds2

10 = e2Ads2 4 + e−2Ads6

K = −3 log(Imρ)

4d EFT:

W = W0+A e

2πiρ N

VD3 = µ4 (Imρ)2

, µ4 ∝ e4Amin

under control if:

e4Amin ⇠ |W0|2 ⌧ 1

+

The KKLT scenario

dS vacuum

Matching with 10d?

hλλi 6= 0

K = −3 log(Imρ)

4d EFT:

W = W0+A e

2πiρ N

VD3 = µ4 (Imρ)2

Tree-level solution + gaugino condensate+ anti-D3-brane

ds2

10 = e2Ads2 4 + e−2Ads6

, µ4 ∝ e4Amin

+

The 10d perspective

Gaugino condensate in 10d? Combination with anti-branes?

Matching 4d-10d vacua:

hλλi 6= 0

[Koerber, L.M. `08] [Dymarsky, L.M. `10] [Baumann, Dymarsky, Kachru, Klebanov, McAllister `10] [Hamada, Hebecker, Shiu, Soler `18-`19] [Moriz, Retolaza Westaphal `17] [Carta, Moritz, Westphal `19] [Gautason, Van Hemelryck, Van Riet, Venken `19] [Bena, Graña, Kovensky, Retolaza `19]

[Kachru, Kim, McAllister, Zimet `19]

The 10d perspective

Gaugino condensate in 10d? Combination with anti-branes?

Matching 4d-10d vacua: Strategy:

hλλi 6= 0

compute 10d: ds2

10 = e2Ads2 4 + e−2Ads6

TMN = T susy

MN + T hλλi MN + T D3 MN

bulk + D7s

integrated 10d EoM:

M 2

P R4

= − Z dvol6

• e−4AgµνTµν + . . .
• <latexit sha1_base64="bqrxixaWwP+HTebsP032nf5g4Tg=">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</latexit>

4Veff

= 4 ⇣ V bulk

eff

+ V hλλi

eff

+ V D3

eff

⌘

Gaugino condensate in 10d?

hλλi 6= 0

Localized gaugino coupling

SD7 ⊃ Z d4σ Z

Σ

dvolΣ λλ (G3 + . . .) · (Ω + . . .)

[Dymarsky, L.M. `10] [Kachru, Kim, McAllister, Zimet `19]

+ Z d4σ Z

Σ

dvolΣ |λλ|2 Ω · Ω

λλ ! hλλi ⇠ e

2πiρ N

+ back-reaction (?)

[Kachru, Kim, McAllister, Zimet `19]

with

W = WKKLT = Z Ω ∧ G3 + Ae

2πiρ N

= M 4

P eK

Kρ¯

ρDρWD¯ ρ ¯

W − 3|W|2

V hλλi

eff

integrating over internal space

= M 4

P eK ⇥

(Kρ¯

ρKρW∂¯ ρ ¯

W + c.c.) + Kρ¯

ρ∂ρW∂¯ ρ ¯

W ⇤

Summing 10d contributions

hλλi 6= 0

Localized gaugino coupling

[Kachru, Kim, McAllister, Zimet `19]

V hλλi

eff

= V susy

KKLT

Anti D3-brane: V D3

eff = V D3 KKLT + (subleading)

probe + backreaction D3

hλλi

Veff = V susy

KKLT + V D3 KKLT

10d-4d match!

[Kachru, Kim, McAllister, Zimet `19]

Hence:

SUSY completion through Goldstino brane or

S2 = 0

Conclusion

Goldistino brane as efficient and natural way to parametrize anti-brane EFT contributions Main weakness: very unconstrained

Main (technical) issue: 10d-4d matching Promising recent progress, but details to be clarified dS from anti-branes require further inspection

E.g. More accurate probe potential from wEFT:

[LM`14-`16]

[Bandos-Heller-Kuzenko-LM- Sorokin`16]

corrected KKLT KKLMMT

e−4A = a + e−4A0

VD3 = M 4

P

(Imρ)3 ⇣ 1 + e−4Amin

Imρ

⌘

e−4Amin ⌧ Imρ

e−4Amin Imρ