Duality and Axionic Weak Gravity Stefano Andriolo KU Leuven [based - - PowerPoint PPT Presentation

Duality and Axionic Weak Gravity

Stefano Andriolo KU Leuven

28th July 2020 StringPheno Summer series

[based on: SA, Huang, Noumi, Ooguri, Shiu ’20 — 2004.13721]

THE SWAMPLAND

Swampland: EFT’s that do not have QG completion Landscape: EFT’s with QG completion Boundary defined by Swampland criteria

[Vafa ’05, Ooguri,Vafa ’06]

WEB OF CONJECTURES

String Lamppost Principle: all consistent QG theories are part of the string landscape Maybe…

[Reviews: Brennan, Carta, Vafa 1711.00864 Palti 1903.06239]

MOTIVATIONS OF OUR WORK Test swampland criteria:

• self-consistency: Linking conjectures in the web
• consistency with other principles

Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,…

Test swampland criteria: Highlight the relevant properties/principles of QG Understand what makes string theory so special (QG unique?)

• self-consistency: Linking conjectures in the web
• consistency with other principles

Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,… “string theory so complete/rich = insurance with full options”

☑ ☑ ☑ ☑ ☑ ☑

MOTIVATIONS OF OUR WORK

Test swampland criteria: Highlight the relevant properties/principles of QG Understand what makes string theory so special (QG unique?)

• self-consistency: Linking conjectures in the web
• consistency with other principles

Unitarity, causality, locality, analyticity, duality, BH physics, SUSY, holography, anomalies,… “string theory so complete/rich = insurance with full options”

☑ ☑ ☑ ☑ ☑ ☑

MOTIVATIONS OF OUR WORK

THE PUNCH-LINE Analyse WGC (axionic version) vs positivity (unitarity, analyticity, locality) Result:

• in simple systems: positivity is sufficient to imply the WGC
• more often: positivity alone is not enough, but specifying

some UV info is sufficient to satisfy the WGC positivity + UV info WGC See also Gregory’s talk on September 1st! (e.g., SL(2,R) symm)

[Cheung,Remmen ’14, Andriolo,Junghans,Noumi,Shiu ’18, Hamada,Noumi,Shiu ’18,…]

[Loges,Noumi,Shiu ’19, ’20] [Heidenreich, Reece,Rudelius ’16, Montero,Shiu,Soler ’16, Aalsma, Cole, Shiu ’19]

OUTLINE Review of WGC and its axionic version (AWGC) Question addressed Illustration of setup Positivity vs AWGC Adding SL(2,R) and implications

WGC and AWGC

Standard formulation of WGC:

• “An EFT with gauge U(1)+gravity is QG-consistent

if it admits at least a state with charge-to-mass ratio greater than that of an extremal black hole (EBH)” qgMP m ≥ 1

since MEBH = gMP QEBH

• Motivated by requiring instability and decay of EBH’s

(here D=4)

• As swampland criterium, trivial for
• Generalized to multiple U(1)’s [Tower/(sub-)lattice

WGC]

• Generalized to other dimensions and abelian p-forms potentials

MP → ∞

g → 0

• Encapsulates “no global symm in QG”, since never satisfied for

[Arkani-Hamed, Motl, Nicolis, Vafa ’06]

[Heidenreich, Reece, Rudelius ’15,’16, Montero,Shiu,Soler ’16, SA, Junghans, Noumi, Shiu ’18]

AWGC is the generalisation to p=0 form potential (=axion):

(here D=4)

form field potential

WGC AWGC

photon axion/2-form dual charged states particles & black holes instantons & grav. instantons coupling relevant quantities mass, charge action, charge gauge coupling

f=axion decay constant

WGC bound

m qgMP < 1

Exists a state s.t.

Sf nMP <O(1)

Extremal obj’s EBH’s regular solutions

[Eucl. wormholes]

Aµ

θ/Bµν

g

1 f

(m, q) (S, q)

Interpretation Instability of EBH’s

tunneling process via collection

• f smaller instantons favoured
• ver single instanton w/ same tot q

OBSERVATION… Higher order (string) corrections modify the classical BH extremality bound in a way that the same EBH’s (Q,M) can be the WGC states classically

M gQMP

Q

M gQMP = 1

Q∗

(semi-classical reasonings)

M MP

macroscopic obj’s

1

Higher order (string) corrections modify the classical BH extremality bound in a way that the same EBH’s (Q,M) can be the WGC states classically

M gQMP

Q

M gQMP = 1

Q∗

(semi-classical reasonings)

M MP

macroscopic obj’s

HO corrections 1

∆M < 0

M gQMP

• HO

= 1 + ∆M gQMP < 1

OBSERVATION…

[Kats, Motl, Padi ’06]

Can the same happen for Euclidean wormholes? 1

Sf nMP

• HO

= 1 + ∆Sf nMP < 1 ?

Sf nMP n

Under which circumstances ? …QUESTION

∆S < 0

SETUP

Classical Axio-dilaton-gravity (ADG)

S = Z d4x√−g R 2 − 1 2(∂µφ)2 − f 2 2 eβφ(∂µθ)2

• Euclidean wormhole solutions (non-singular class of solutions for )

r = r0

can be regarded as instanton—anti-instanton pair Axion-gravity (AG)

β = 0

ds2 = dr2 1 − r4

r4

+ r2dΩ2

3

r4

0 = n2f 2

24π4 cos2 h √

6 4 β · π 2

i

S = 2|n|MP βf sin h √

6 4 β · π 2

i

√ 6 4 π · |n|MP f

semiwormhole (instanton) action

β = 0

β < 4 √ 6

[reviews: Hebecker,Mangat,Theisen,Witkowski ’16, Hebecker-Mikhail-Soler ’18, Van Riet ’20]

Classical Axio-dilaton-gravity (ADG)

S = Z d4x√−g R 2 − 1 2(∂µφ)2 − f 2 2 eβφ(∂µθ)2

• Euclidean wormhole solutions (non-singular class of solutions for )

Axion-gravity (AG)

β = 0

β < 4 √ 6

+ HO (4-derivative) corrections, generic

∆S = Z d4x√−g h a1(φ)(∂µφ∂µφ)2 + a2(φ)f 4(∂µθ∂µθ)2 + a3(φ)f 2(∂µφ∂µφ)(∂µθ∂µθ) + a4(φ)f 2(∂µφ∂µθ)2 + a5(φ)W 2 + a6θW ˜ W i

Evaluation of gives…

∆S

• AG system :

β = 0

∆S = −24π2a2

• ADG system

∆S = 36π2 Z

π 2

dt cos3 t  − a1

• φ(t)
• tan4 h √

6 4 β · t

i − a2

• φ(t)
• e−2βφ(t) sec4 h √

6 4 β · t

i + ⇣ a3

• φ(t)
• + a4
• φ(t)

⌘ e−βφ(t) tan2 h √

6 4 β · t

i sec2 h √

6 4 β · t

i

• AG system :

β = 0

∆S = −24π2a2

• ADG system

∆S = 36π2 Z

π 2

dt cos3 t  − a1

• φ(t)
• tan4 h √

6 4 β · t

i − a2

• φ(t)
• e−2βφ(t) sec4 h √

6 4 β · t

i + ⇣ a3

• φ(t)
• + a4
• φ(t)

⌘ e−βφ(t) tan2 h √

6 4 β · t

i sec2 h √

6 4 β · t

i

a1 ≥ 0 , a2 ≥ 0 , a4 ≥ 0 , −a4 − 2√a1a2 ≤ a3 ≤ 2√a1a2

we can use positivity conditions to determine (for any bg )

φ = φ∗

• AG system :

β = 0

∆S = −24π2a2

• ADG system

∆S = 36π2 Z

π 2

dt cos3 t  − a1

• φ(t)
• tan4 h √

6 4 β · t

i − a2

• φ(t)
• e−2βφ(t) sec4 h √

6 4 β · t

i + ⇣ a3

• φ(t)
• + a4
• φ(t)

⌘ e−βφ(t) tan2 h √

6 4 β · t

i sec2 h √

6 4 β · t

i

a1 ≥ 0 , a2 ≥ 0 , a4 ≥ 0 , −a4 − 2√a1a2 ≤ a3 ≤ 2√a1a2

we can use positivity conditions to determine (for any bg )

φ = φ∗

< 0

• AG system :

β = 0

• ADG system

∆S = 36π2 Z

π 2

dt cos3 t  − a1

• φ(t)
• tan4 h √

6 4 β · t

i − a2

• φ(t)
• e−2βφ(t) sec4 h √

6 4 β · t

i + ⇣ a3

• φ(t)
• + a4
• φ(t)

⌘ e−βφ(t) tan2 h √

6 4 β · t

i sec2 h √

6 4 β · t

i

a1 ≥ 0 , a2 ≥ 0 , a4 ≥ 0 , −a4 − 2√a1a2 ≤ a3 ≤ 2√a1a2

we can use positivity conditions to determine (for any bg )

φ = φ∗

Q 0

?

Simplified illustration (in the plane)

a2 = a1

Prohibited by positivity Satisfy positivity, but WGC violated Satisfy positivity and WGC model-dep

a3 a4 −2a1 2a1

∆S < 0

∆S > 0

∆S = −24π2a2

generically, follows from unitarity, analyticity, locality

• f UV scattering amplitudes

and the sing of is related to the sign of propagator (unitarity) where, for instance, arises after integrating out massive scalar POSITIVITY INTERMEZZO (presto)

ℒ = − 1 2(∂μa)2 + α (∂μa∂μa)2 + ⋯ α ϕ ϕ (∂μa)2 g g

1 m2 + p2

ϕ a a a a a a a a α = g2 2m2 ≥ 0 α

[Hamada-Noumi-Shiu ’18]

|α| > 1/(M2

s M2 Pl)

Axion-gravity EFT

α > 0

• Caveat, assumption: gravitational Regge states are sub-dominant

[Adams, Arkani-Hamed, Dubovsky, Nicolis, Rattazzi ’06]

Back to the ADG system: Can we assume some additional property and show that

∆S < 0 ?

SL(2,R) SYMMETRY Symmetry of the 2-derivative action Extended to the HO 4-derivative action terms:

• nly two SL(2,R) invariant operators

τ → aτ + b cτ + d (a, b, c, d ∈ R, ad − bc = 1)

τ = β 2 fθ + ie− β

2 φ

λ1,2 = const

λ1 (∂µτ∂µ¯ τ)2 ⇣

β 2

⌘4 (Imτ)4 + λ2 (∂µτ∂µτ)(∂µ¯ τ∂µ¯ τ) ⇣

β 2

⌘4 (Imτ)4

4d parameter space 2d parameter space

(a1, a2, a3, a4) (λ1, λ2)

We are adding structure to EFT [=SL(2,Z)+axion shift symm]

“duality”

∆S = −24π2(λ1 + λ2)

Positivity means

λ1 + λ2 ≥ 0 λ2 ≥ 0

Evaluation of gives…

∆S

∆S = −24π2(λ1 + λ2)

Positivity means

λ1 + λ2 ≥ 0 λ2 ≥ 0

Evaluation of gives…

∆S

< 0

∆S = −24π2(λ1 + λ2)

Positivity means

λ1 + λ2 ≥ 0 λ2 ≥ 0

a3 a4 2a1 −2a1

a2 = a1

Prohibited by positivity Satisfy positivity, but WGC violated Satisfy positivity and WGC model-dep SL(2,R) symmetry

a1 = a2 = λ1 + λ2 a3 + a4 = 2a1

Evaluation of gives…

∆S

< 0

CONCLUSION

SUMMARY AND OUTLOOK We did it by studying relationship AWGC vs positivity* in A(D)G:

• In absence of dilaton: positivity implies AWGC
• With a dilaton: positivity is not enough. In particular, there is a

region in the EFT parameter space where WGC is violated even if positivity is satisfied! Are there other UV inputs useful to demonstrate WGC? [see Gregory’s talk]

• Enriching the EFT structure with SL(2,R) is sufficient for AWGC

(i.e., the EFT lies in the region satisfying the AWGC) We provided some evidence for AWGC (relevant for pheno: inflation,…) *caveat on Regge states Work on this direction to find which UV properties are necessary/sufficient for WGC or other swampland conjectures: Can we find “what makes string theory tick”? (relevant features)

Thank you